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  • Persistence of normally hyperbolic invariant manifolds in the absence of rate conditions
    Nonlinearity (IF 1.505) Pub Date : 2020-08-04
    Maciej J Capiński and Hieronim Kubica

    We consider perturbations of normally hyperbolic invariant manifolds, under which they can lose their hyperbolic properties. We show that if the perturbed map which drives the dynamical system preserves the properties of topological expansion and contraction, then the manifold is perturbed to an invariant set. The main feature is that our results do not require the rate conditions to hold after the

    更新日期:2020-08-06
  • On singularities of stationary isometric deformations
    Nonlinearity (IF 1.505) Pub Date : 2020-08-04
    Peter Eberhard and Peter Hornung

    Unstretchable thin elastic plates such as paper can be modelled as intrinsically flat W 2,2 isometric immersions from a domain in ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4900/nonab9245ieqn1.gif] {${\mathbb{R}}^{2}$} into ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4900/nonab9245ieqn2.gif] {${\mathbb{R}}^{3}$} . In previous work it has been shown that if such an isometric immersion minimizes

    更新日期:2020-08-05
  • Discretization and superintegrability all rolled into one
    Nonlinearity (IF 1.505) Pub Date : 2020-08-04
    A V Tsiganov

    Abelian integrals appear in mathematical descriptions of various physical processes. According to Abel’s theorem these integrals are related to motion of a set of points along a plane curve around fixed points, which are rarely used in physical applications. We propose to interpret coordinates of the fixed points either as parameters of exact discretization or as additional first integrals for equations

    更新日期:2020-08-05
  • A probabilistic Takens theorem
    Nonlinearity (IF 1.505) Pub Date : 2020-08-04
    Krzysztof Barański, Yonatan Gutman and Adam Śpiewak

    Let ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4940/nonab8fb8ieqn1.gif] {$X\subset {\mathbb{R}}^{N}$} be a Borel set, μ a Borel probability measure on X and T : X → X a locally Lipschitz and injective map. Fix ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4940/nonab8fb8ieqn2.gif] {$k\in \mathbb{N}$} strictly greater than the (Hausdorff) dimension of X and assume that the set of p -periodic

    更新日期:2020-08-05
  • Bounding extrema over global attractors using polynomial optimisation
    Nonlinearity (IF 1.505) Pub Date : 2020-08-04
    David Goluskin

    We present a framework for bounding extreme values of quantities on global attractors of differential dynamical systems. A global attractor is the minimal set that attracts all bounded sets; it contains all forward-time limit points. Our approach uses (generalised) Lyapunov functions to find attracting sets, which must contain the global attractor, and the choice of Lyapunov function is optimised based

    更新日期:2020-08-05
  • Regularity results for rough solutions of the incompressible Euler equations via interpolation methods
    Nonlinearity (IF 1.505) Pub Date : 2020-08-02
    Maria Colombo, Luigi De Rosa and Luigi Forcella

    Given any solution u of the Euler equations which is assumed to have some regularity in space—in terms of Besov norms, natural in this context—we show by interpolation methods that it enjoys a corresponding regularity in time and that the associated pressure p is twice as regular as u . This generalizes a recent result by Isett (2003 arXiv:1307.056517) (see also Colombo and De Rosa (2020 SIAM J. Math

    更新日期:2020-08-03
  • Rapidly rotating white dwarfs
    Nonlinearity (IF 1.505) Pub Date : 2020-08-02
    Walter A Strauss and Yilun Wu

    A rotating star may be modeled as a continuous system of particles attracted to each other by gravity and with a given total mass and prescribed angular velocity. Mathematically this leads to the Euler–Poisson system. A white dwarf star is modeled by a very particular, and rather delicate, equation of state for the pressure as a function of the density. We prove an existence theorem for rapidly rotating

    更新日期:2020-08-03
  • Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations
    Nonlinearity (IF 1.505) Pub Date : 2020-08-02
    Jana de Wiljes and Xin T Tong

    Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For spatial–temporal models, the ensemble Kalman filter with proper localisation techniques is considered to be a state-of-the-art DA methodology. This article proposes and investigates

    更新日期:2020-08-03
  • A nonlinear quantum adiabatic approximation
    Nonlinearity (IF 1.505) Pub Date : 2020-08-02
    Clotilde Fermanian-Kammerer and Alain Joye

    This paper is devoted to a generalisation of the quantum adiabatic theorem to a nonlinear setting. We consider a Hamiltonian operator which depends on the time variable and on a finite number of parameters and acts on a separable Hilbert space of which we select a fixed basis. We study an evolution equation in which this Hamiltonian acts on the unknown vector, while depending on coordinates of the

    更新日期:2020-08-03
  • Asymptotic decoupling and weak Gibbs measures for finite alphabet shift spaces
    Nonlinearity (IF 1.505) Pub Date : 2020-08-02
    C-E Pfister and W G Sullivan

    For the space X in a large class of finite alphabet shift spaces (lattice models) and the class of functions f with bounded total oscillations, we prove that each equilibrium measure ν at f = φ is a weak Gibbs measures for φ − P ( φ ). In addition, the empirical measures satisfy a full large deviations principle for ( X , ν ).

    更新日期:2020-08-03
  • Sharp time decay rates of H 1 weak solutions for the 2D MHD equations with linear damping velocity
    Nonlinearity (IF 1.505) Pub Date : 2020-08-02
    Hailong Ye, Yan Jia and Bo-Qing Dong

    This study is concerned with the large time decay rates of the H 1 weak solutions for the 2D magnetohydrodynamic equations with linear damping velocity. Due to the inconsistencies of the dissipative effects between linear velocity and Laplacian magnetic diffusion, neither the classic Fourier splitting method nor Kato’s method is available directly. By developing an alternative analysis argument together

    更新日期:2020-08-03
  • Well-posedness of a Schrödinger–Poisson model describing nonlinear chiral effects
    Nonlinearity (IF 1.505) Pub Date : 2020-08-02
    José Luis López

    The purpose of this paper is to investigate the well-posedness in the (weighted) energy space of a Schrödinger–Poisson model with additional chiral nonlinearity proportional to the electric current ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4837/nonab8fb4ieqn1.gif] {$j\left[\psi \right]=\mathrm{I}\mathrm{m}\left(\overline{\psi }{\psi }_{x}\right)$} . More precisely, a unique mild solution of

    更新日期:2020-08-03
  • Contour dynamics for surface quasi-geostrophic fronts
    Nonlinearity (IF 1.505) Pub Date : 2020-07-28
    John K Hunter, Jingyang Shu and Qingtian Zhang

    We derive contour dynamics equations for the motion of infinite planar surface quasi-geostrophic fronts that can be represented as a graph. We give two different derivations with the same result: one is based on a decomposition of the front velocity field into a shear flow and a perturbation that decays away from the front; the other is based on the interpretation of the Riesz transform of the piecewise-constant

    更新日期:2020-07-29
  • Critical base for the unique codings of fat Sierpinski gasket
    Nonlinearity (IF 1.505) Pub Date : 2020-07-22
    Derong Kong and Wenxia Li

    Given β ∈ (1, 2) the fat Sierpinski gasket ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4484/nonab8bafieqn1.gif] {${\mathcal{S}}_{\beta }$} is the self-similar set in ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4484/nonab8bafieqn2.gif] {${\mathbb{R}}^{2}$} generated by the iterated function system (IFS) ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4484/nonab8bafieqn3.gif] {${f}_{\beta

    更新日期:2020-07-23
  • Third order open mapping theorems and applications to the end-point map
    Nonlinearity (IF 1.505) Pub Date : 2020-07-22
    Francesco Boarotto, Roberto Monti and Francesco Palmurella

    This paper is devoted to a third order study of the end-point map in sub-Riemannian geometry. We first prove third order open mapping results for maps from a Banach space into a finite dimensional manifold. In a second step, we compute the third order term in the Taylor expansion of the end-point map and we specialize the abstract theory to the study of length-minimality of sub-Riemannian strictly

    更新日期:2020-07-23
  • Super-critical Neumann problems on unbounded domains
    Nonlinearity (IF 1.505) Pub Date : 2020-07-22
    Claudianor O Alves and Abbas Moameni

    In this paper, by making use of a new variational principle, we prove existence of nontrivial solutions for two different types of semilinear problems with Neumann boundary conditions in unbounded domains. Namely, we study elliptic equations and Hamiltonian systems on the unbounded domain ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4568/nonab8bacieqn1.gif] {${\Omega}={\mathbb{R}}^{m}{\times}{B}_{r}$}

    更新日期:2020-07-23
  • Uniform recurrence properties for beta-transformation
    Nonlinearity (IF 1.505) Pub Date : 2020-07-22
    Lixuan Zheng and Min Wu

    For any β > 1, let T β : [0, 1) → [0, 1) be the β -transformation defined by T β x = βx mod 1. We study the uniform recurrence properties of the orbit of a point under the β -transformation to the point itself. The size of the set of points with prescribed uniform recurrence rate is obtained. More precisely, for any ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4590/nonab8a65ieqn1.gif] {$0{\leq

    更新日期:2020-07-23
  • Global well-posedness for the Euler alignment system with mildly singular interactions
    Nonlinearity (IF 1.505) Pub Date : 2020-07-22
    Jing An and Lenya Ryzhik

    We consider the Euler alignment system with mildly singular interaction kernels. When the local repulsion term is of the fractional type, global in time existence of smooth solutions was proved in [16, 22–24]. Here, we consider a class of less singular interaction kernels and establish the global regularity of solutions as long as the interaction kernels are not integrable. The proof relies on modulus

    更新日期:2020-07-23
  • Steady incompressible axially symmetric Réthy flows
    Nonlinearity (IF 1.505) Pub Date : 2020-07-22
    Jianfeng Cheng, Lili Du and Wei Xiang

    In this paper, we are concerned with a jet and a cavity issuing from a semi-infinite long nozzle around a given obstacle in the axially symmetric case, which is called the axially symmetric incompressible Réthy flow. The existence and uniqueness of the axially symmetric Réthy flow are obtained via a variational approach when the nozzle and the obstacle are y -graphs and a mass flux at the inlet of

    更新日期:2020-07-23
  • Analysis of a West Nile virus model with nonlocal diffusion and free boundaries
    Nonlinearity (IF 1.505) Pub Date : 2020-07-22
    Yihong Du and Wenjie Ni

    We consider a West Nile virus model with nonlocal diffusion and free boundaries, in the form of a cooperative evolution system that can be viewed as a nonlocal version of the free boundary model of Lin and Zhu (2017 J . Math . Biol . 75 1381–1409). The model is a representative of a class of ‘vector-host’ models. We prove that this nonlocal model is well-posed, and its long-time dynamical behaviour

    更新日期:2020-07-23
  • Effect of driving on coarsening dynamics in phase-separating systems
    Nonlinearity (IF 1.505) Pub Date : 2020-07-22
    D Tseluiko, M Alesemi, T-S Lin and U Thiele

    We consider the Cahn–Hilliard (CH) equation with a Burgers-type convective term that is used as a model of coarsening dynamics in laterally driven phase-separating systems. In the absence of driving, it is known that solutions to the standard CH equation are characterized by an initial stage of phase separation into regions of one phase surrounded by the other phase (i.e. clusters or drops/holes or

    更新日期:2020-07-23
  • Sphere branched coverings and the growth rate inequality
    Nonlinearity (IF 1.505) Pub Date : 2020-07-22
    J Iglesias, A Portela, A Rovella and J Xavier

    We show that the growth rate inequality ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4613/nonab8773ieqn1.gif] {$\mathrm{lim}\;sup\frac{1}{n}\;\mathrm{log}\left(\#\mathrm{F}\mathrm{i}\mathrm{x}\left({f}^{n}\right)\right){\geqslant}\mathrm{log}\;d$} holds for branched coverings of degree d of the sphere S 2 having a completely invariant simply connected region R with locally connected boundary, except

    更新日期:2020-07-23
  • Periodic solutions and invariant torus in the Rössler system
    Nonlinearity (IF 1.505) Pub Date : 2020-07-22
    Murilo R Cândido, Douglas D Novaes and Claudia Valls

    The Rössler system is characterized by a three-parameter family of quadratic 3D vector fields. There exist two one-parameter families of Rössler systems exhibiting a zero-Hopf equilibrium. For Rössler systems near to one of these families, we provide generic conditions ensuring the existence of a torus bifurcation. In this case, the torus surrounds a periodic solution that bifurcates from the zero-Hopf

    更新日期:2020-07-23
  • Global dynamics and travelling waves for a periodic and diffusive chemostat model with two nutrients and one microorganism
    Nonlinearity (IF 1.505) Pub Date : 2020-07-21
    Wei Wang, Wanbiao Ma and Zhaosheng Feng

    We consider a classical chemostat model with two nutrients and one microorganism, which incorporates spatial diffusion, temporal heterogeneity, and spatial heterogeneity. We study the basic reproduction number R 0 and the asymptotic behaviours, which provide us some new findings in chemostat models. Global dynamics in terms of R 0 is investigated in a bounded spatial domain. In the general situation

    更新日期:2020-07-22
  • Existence of noise induced order, a computer aided proof
    Nonlinearity (IF 1.505) Pub Date : 2020-07-21
    Stefano Galatolo, Maurizio Monge and Isaia Nisoli

    We prove the existence of noise induced order in the Matsumoto–Tsuda model, where it was originally discovered in 1983 by numerical simulations. This is a model of the famous Belousov–Zhabotinsky reaction, a chaotic chemical reaction, and consists of a one dimensional random dynamical system with additive noise. The simulations showed that an increase in amplitude of the noise causes the Lyapunov exponent

    更新日期:2020-07-22
  • Global stability properties of the climate: Melancholia states, invariant measures, and phase transitions
    Nonlinearity (IF 1.505) Pub Date : 2020-07-21
    Valerio Lucarini and Tamás Bódai

    For a wide range of values of the intensity of the incoming solar radiation, the Earth features at least two attracting states, which correspond to competing climates. The warm climate is analogous to the present one; the snowball climate features global glaciation and conditions that can hardly support life forms. Paleoclimatic evidences suggest that in the past our planet flipped between these two

    更新日期:2020-07-22
  • Renormalization and universality of the Hofstadter spectrum
    Nonlinearity (IF 1.505) Pub Date : 2020-07-21
    Hans Koch and Saša Kocić

    We consider a renormalization transformation ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4381/nonab8693ieqn1.gif] {$\mathfrak{R}$} for skew-product maps of the type that arise in a spectral analysis of the Hofstadter Hamiltonian. Periodic orbits of ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4381/nonab8693ieqn2.gif] {$\mathfrak{R}$} determine universal constants analogous to the critical

    更新日期:2020-07-22
  • Topological sensitivities via a Lagrangian approach for semilinear problems
    Nonlinearity (IF 1.505) Pub Date : 2020-07-21
    Kevin Sturm

    In this paper we present a methodology that allows the efficient computation of the topological derivative for semilinear elliptic problems within the averaged adjoint Lagrangian framework. The generality of our approach should also allow the extension to evolutionary and other nonlinear problems. Our strategy relies on a rescaled differential quotient of the averaged adjoint state variable which we

    更新日期:2020-07-22
  • Forward boundedness of the trace map for the period doubling substitution
    Nonlinearity (IF 1.505) Pub Date : 2020-07-21
    T O Carvalho

    We study the trace map for the period doubling substitution, proving its orbits are forward bounded, a sufficient condition for application in the study of spectral measures. This result is in contrast with some recent findings of unbounded orbits on the trace map for the Thue–Morse substitution.

    更新日期:2020-07-22
  • Forwards attraction properties in scalar non-autonomous linear–dissipative parabolic PDEs. The case of null upper Lyapunov exponent
    Nonlinearity (IF 1.505) Pub Date : 2020-07-21
    José A Langa, Rafael Obaya and Ana M Sanz

    As it is well-known, the forwards and pullback dynamics are in general unrelated. In this paper we present an in-depth study of whether the pullback attractor is also a forwards attractor for the processes involved with the skew-product semiflow induced by a family of scalar non-autonomous reaction–diffusion equations which are linear in a neighbourhood of zero and have null upper Lyapunov exponent

    更新日期:2020-07-22
  • Integrability, exact reductions and special solutions of the KP–Whitham equations
    Nonlinearity (IF 1.505) Pub Date : 2020-07-09
    Gino Biondini, Mark A Hoefer and Antonio Moro

    Reductions of the KP–Whitham system, namely the (2+1)-dimensional hydrodynamic system of five equations that describes the slow modulations of periodic solutions of the Kadomtsev–Petviashvili (KP) equation, are studied. Specifically, the soliton and harmonic wave limits of the KP–Whitham system are considered, which give rise in each case to a four-component (2+1)-dimensional hydrodynamic system. It

    更新日期:2020-07-10
  • Unique continuation principles for a higher order fractional Laplace equation
    Nonlinearity (IF 1.505) Pub Date : 2020-07-09
    Veronica Felli and Alberto Ferrero

    In this paper we prove the strong unique continuation principle and the unique continuation from sets of positive measure for solutions of a higher order fractional Laplace equation in an open domain. Our proofs are based on the Caffarelli–Silvestre (2007 Commun. PDE 32 1245–60) extension method combined with an Almgren type monotonicity formula. The corresponding extended problem is formulated as

    更新日期:2020-07-10
  • Convergence of a Robin boundary approximation for a Cahn–Hilliard system with dynamic boundary conditions
    Nonlinearity (IF 1.505) Pub Date : 2020-07-09
    Patrik Knopf and Kei Fong Lam

    We prove the existence of unique weak solutions to an extension of a Cahn–Hilliard model proposed recently by C Liu and H Wu (2019 Arch. Ration. Mech. Anal. 233 167–247), in which the new dynamic boundary condition is further generalised with an affine linear relation between the surface and bulk phase field variables. As a first approach to tackle more general and nonlinear relations, we investigate

    更新日期:2020-07-10
  • Large time behavior for a compressible two-fluid model with algebraic pressure closure and large initial data
    Nonlinearity (IF 1.505) Pub Date : 2020-07-05
    Yang Li, Yongzhong Sun and Ewelina Zatorska

    In this paper, we consider a compressible two-fluid system with a common velocity field and algebraic pressure closure in dimension one. Existence, uniqueness and stability of global weak solutions to this system are obtained with arbitrarily large initial data. Making use of the uniform-in-time bounds for the densities from above and below, exponential decay of weak solution to the unique steady state

    更新日期:2020-07-06
  • Martingale approximations and anisotropic Banach spaces with an application to the time-one map of a Lorentz gas
    Nonlinearity (IF 1.505) Pub Date : 2020-07-05
    Mark Demers, Ian Melbourne and Matthew Nicol

    In this paper, we show how the Gordin martingale approximation method fits into the anisotropic Banach space framework. In particular, for the time-one map of a finite horizon planar periodic Lorentz gas, we prove that Hölder observables satisfy statistical limit laws such as the central limit theorem and associated invariance principles. Previously, these properties were known only for a restricted

    更新日期:2020-07-06
  • Nonlinear and nonlocal eigenvalue problems: variational existence, decay properties, approximation, and universal scaling limits
    Nonlinearity (IF 1.505) Pub Date : 2020-07-05
    Michael Herrmann and Karsten Matthies

    We study a class of nonlinear eigenvalue problems which involves a convolution operator as well as a superlinear nonlinearity. Our variational existence proof is based on constrained optimization and provides a one-parameter family of solutions with positive eigenvalues and unimodal eigenfunctions. We also discuss the decay properties and the numerical computations of those eigenfunctions, and conclude

    更新日期:2020-07-06
  • The ponderomotive Lorentz force
    Nonlinearity (IF 1.505) Pub Date : 2020-06-18
    Graham Cox and Mark Levi

    This paper describes a curious phenomenon: a particle in a rapidly varying potential is subject to an effective magnetic-like force. This force is in addition to the well-known ponderomotive force, but it has not been shown to exist before except for the linear case of a rapidly rotating quadratic saddle potential. We show that this is a universal phenomenon: the magnetic-like force arises generically

    更新日期:2020-06-19
  • Variational approach of critical sharp front speeds in degenerate diffusion model with time delay
    Nonlinearity (IF 1.505) Pub Date : 2020-06-14
    Tianyuan Xu, Shanming Ji, Ming Mei and Jingxue Yin

    For the classical reaction diffusion equation, the a priori speed of fronts is determined exactly in the pioneering paper (Benguria and Depassier 1996 Commun. Math. Phys. 175 221–227) by variational characterization method. In this paper, we study the age-structured population dynamics using a degenerate diffusion equation with time delay. We show the existence and uniqueness of sharp critical fronts

    更新日期:2020-06-14
  • Positive transversality via transfer operators and holomorphic motions with applications to monotonicity for interval maps
    Nonlinearity (IF 1.505) Pub Date : 2020-06-14
    Genadi Levin, Weixiao Shen and Sebastian van Strien

    In this paper we will develop a general approach which shows that generalized ‘critical relations’ of families of locally defined holomorphic maps on the complex plane unfold transversally. The main idea is to define a transfer operator, which is a local analogue of the Thurston pullback operator, using holomorphic motions. Assuming a so-called lifting property is satisfied, we obtain information about

    更新日期:2020-06-14
  • The impact of multiplicative noise in SPDEs close to bifurcation via amplitude equations
    Nonlinearity (IF 1.505) Pub Date : 2020-06-11
    Dirk Blömker and Hongbo Fu

    This article deals with the approximation of a stochastic partial differential equation (SPDE) via amplitude equations. We consider an SPDE with a cubic nonlinearity perturbed by a general multiplicative noise that preserves the constant trivial solution and we study the dynamics around it for the deterministic equation being close to a bifurcation. Based on the separation of time-scales close to a

    更新日期:2020-06-11
  • Existence of global solutions for isentropic gas flow with friction
    Nonlinearity (IF 1.505) Pub Date : 2020-06-11
    Yun-guang Lu

    In this paper, we study the existence of global entropy solutions for the Cauchy problem of the extended river flow system with a friction α ( x ) depending on the space variable x . First, under the boundedness of ##IMG## [http://ej.iop.org/images/0951-7715/33/8/3940/nonab7d20ieqn1.gif] {${\vert \alpha \left(x\right)\vert }_{{L}^{1}\left(R\right)}$} , we apply the viscosity-flux approximation method

    更新日期:2020-06-11
  • Stratified equatorial flows in cylindrical coordinates
    Nonlinearity (IF 1.505) Pub Date : 2020-06-11
    D Henry and C I Martin

    We construct an exact solution modelling the geophysical dynamics of an inviscid and incompressible fluid which possesses a variable density stratification, where the fluid density may vary with both the depth and latitude. Our solution pertains to the large-scale equatorial dynamics of a fluid body with a free surface propagating steadily in a purely azimuthal direction, and is expressed in terms

    更新日期:2020-06-11
  • Laplacian of the distance function on the cut locus on a Riemannian manifold
    Nonlinearity (IF 1.505) Pub Date : 2020-06-11
    François Générau

    In this note, we prove that, on a Riemannian manifold M , the Laplacian of the distance function to a point b is −∞ in the sense of barriers, at every point of the cut locus of M with respect to b . We apply this result to an obstacle-type variational problem where the obstacle is the distance function. It allows us to replace the latter with a smoother obstacle.

    更新日期:2020-06-11
  • Mumford–Shah functionals on graphs and their asymptotics
    Nonlinearity (IF 1.505) Pub Date : 2020-06-08
    Marco Caroccia, Antonin Chambolle and Dejan Slepčev

    We consider adaptations of the Mumford–Shah functional to graphs. These are based on discretizations of nonlocal approximations to the Mumford–Shah functional. Motivated by applications in machine learning we study the random geometric graphs associated to random samples of a measure. We establish the conditions on the graph constructions under which the minimizers of graph Mumford–Shah functionals

    更新日期:2020-06-08
  • Variational order for forced Lagrangian systems II. Euler–Poincaré equations with forcing
    Nonlinearity (IF 1.505) Pub Date : 2020-06-08
    D Martín de Diego and R T Sato Martín de Almagro

    In this paper we provide a variational derivation of the Euler–Poincaré equations for systems subjected to external forces using an adaptation of the techniques introduced by Galley and others Martín de Diego and Martín de Almagro (2018 Nonlinearity 31 3814–3846), Galley (2013 Phys. Rev. Lett. 110 174301), Galley et al (2014 (arXiv:[math-Ph] 1412.3082)). Moreover, we study in detail the underlying

    更新日期:2020-06-08
  • Long time asymptotics for homoenergetic solutions of the Boltzmann equation. Hyperbolic-dominated case
    Nonlinearity (IF 1.505) Pub Date : 2020-06-08
    Richard D James, Alessia Nota and Juan J L Velázquez

    In this paper we continue the formal analysis of the long-time asymptotics of the homoenergetic solutions for the Boltzmann equation that we began by James et al (2019 J. Nonlinear Sci. 29 1943–73). They have the form ##IMG## [http://ej.iop.org/images/0951-7715/33/8/3781/nonab853fieqn1.gif] {$f\left(x,v,t\right)=g\left(v-L\left(t\right)x,t\right)$} where ##IMG## [http://ej.iop.org/images/0951-7715

    更新日期:2020-06-08
  • Measure-theoretic equicontinuity and rigidity
    Nonlinearity (IF 1.505) Pub Date : 2020-06-08
    Fangzhou Cai

    Let ( X , T ) be a topological dynamical system and μ ∈ M ( X , T ). We show that ##IMG## [http://ej.iop.org/images/0951-7715/33/8/3739/nonab8a67ieqn1.gif] {$\left(X,\mathcal{B},\mu ,T\right)$} is rigid if and only if there exists some subsequence A of ##IMG## [http://ej.iop.org/images/0951-7715/33/8/3739/nonab8a67ieqn2.gif] {$\mathbb{N}$} such that ( X , T ) is μ – A -equicontinuous if and only if

    更新日期:2020-06-08
  • Long time existence of classical solutions for the rotating Euler equations and related models in the optimal Sobolev space
    Nonlinearity (IF 1.505) Pub Date : 2020-06-08
    Houyu Jia and Renhui Wan

    Koh Y et al (2014 J. Differ. Equ. 256 704–44) proved the long time existence of classical solutions to the 3D rotating Euler equations for initial data in the Sobolev space ##IMG## [http://ej.iop.org/images/0951-7715/33/8/3763/nonab86cfieqn1.gif] {${H}^{s}\left({\mathbb{R}}^{3}\right)$} ( s > 7/2). Here we improve their assumed regularity and weaken the lower bound of the rotating speed by establishing

    更新日期:2020-06-08
  • Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects
    Nonlinearity (IF 1.505) Pub Date : 2020-06-08
    Yuan Gao, Jian-Guo Liu, Jianfeng Lu and Jeremy L Marzuola

    We study a 4th order degenerate parabolic PDE model in one-dimension with a 2nd order correction modeling the evolution of a crystal surface under the influence of both thermal fluctuations and evaporation/deposition effects. First, we provide a non-rigorous derivation of the PDE from an atomistic model using variations on kinetic Monte Carlo rates proposed by the last author with Weare [Marzuola J

    更新日期:2020-06-08
  • Localized patterns in planar bistable weakly coupled lattice systems
    Nonlinearity (IF 1.505) Pub Date : 2020-06-01
    Jason J Bramburger and Björn Sandstede

    Localized planar patterns in spatially extended bistable systems are known to exist along intricate bifurcation diagrams, which are commonly referred to as snaking curves. Their analysis is challenging as techniques such as spatial dynamics that have been used to explain snaking in one space dimension no longer work in the planar case. Here, we consider bistable systems posed on square lattices and

    更新日期:2020-06-01
  • Discrete nonlocal nonlinear Schrödinger systems: Integrability, inverse scattering and solitons
    Nonlinearity (IF 1.505) Pub Date : 2020-06-01
    Mark J Ablowitz, Xu-Dan Luo and Ziad H Musslimani

    A number of integrable nonlocal discrete nonlinear Schrödinger (NLS) type systems have been recently proposed. They arise from integrable symmetry reductions of the well-known Ablowitz–Ladik scattering problem. The equations include: the classical integrable discrete NLS equation, integrable nonlocal: PT symmetric, reverse space time (RST), and the reverse time (RT) discrete NLS equations. Their mathematical

    更新日期:2020-06-01
  • Asymptotic analysis of a nonlinear eigenvalue problem arising in electromagnetics
    Nonlinearity (IF 1.505) Pub Date : 2020-06-01
    D V Valovik

    An eigenvalue problem for Maxwell’s equations with anisotropic cubic nonlinearity is studied. The problem describes propagation of transverse magnetic waves in a dielectric layer filled with (nonlinear) anisotropic Kerr medium. The nonlinearity involves two non-negative parameters a , b that are usually small. In the case a = b = 0 one arrives at a linear problem that has a finite number of solutions

    更新日期:2020-06-01
  • On the return to equilibrium problem for axisymmetric floating structures in shallow water
    Nonlinearity (IF 1.505) Pub Date : 2020-06-01
    Edoardo Bocchi

    In this paper we address the return to equilibrium problem for an axisymmetric floating structure in shallow water. First we show that the equation for the solid motion can be reduced to a delay differential equation involving an extension–trace operator whose role is to describe the influence of the fluid equations on the solid motion. It turns out that the compatibility conditions on the initial

    更新日期:2020-06-01
  • On the topology of nearly-integrable Hamiltonians at simple resonances
    Nonlinearity (IF 1.505) Pub Date : 2020-06-01
    L Biasco and L Chierchia

    We show that, in general, averaging at simple resonances a real-analytic, nearly-integrable Hamiltonian, one obtains a one-dimensional system with a cosine-like potential; ‘in general’ means for a generic class of holomorphic perturbations and apart from a finite number of simple resonances with small Fourier modes; ‘cosine-like’ means that the potential depends only on the resonant angle, with respect

    更新日期:2020-06-01
  • An alphabetical approach to Nivat’s conjecture
    Nonlinearity (IF 1.505) Pub Date : 2020-06-01
    Cleber F Colle and Eduardo Garibaldi

    Since techniques used to address the Nivat’s conjecture usually rely on Morse–Hedlund theorem, an improved version of this classical result may mean a new step towards a proof for the conjecture. In this paper, considering an alphabetical version of the Morse–Hedlund theorem, we show that, for a configuration ##IMG## [http://ej.iop.org/images/0951-7715/33/7/3620/nonab7638ieqn1.gif] {$\eta \in {A}^

    更新日期:2020-06-01
  • Shrinking targets for non-autonomous systems
    Nonlinearity (IF 1.505) Pub Date : 2020-06-01
    Marco Antonio López

    In the present work we establish a Bowen-type formula for the Hausdorff dimension of shrinking target sets for non-autonomous conformal iterated function systems in arbitrary dimensions and satisfying certain conditions. In the case of dimension 1 we also investigate non-linear perturbations of linear systems and obtain sufficient conditions under which the perturbed systems satisfy the conditions

    更新日期:2020-06-01
  • The profile of chiral skyrmions of small radius
    Nonlinearity (IF 1.505) Pub Date : 2020-05-28
    Stavros Komineas, Christof Melcher and Stephanos Venakides

    Chiral skyrmions are stable particle-like solutions of the Landau–Lifshitz equation for ferromagnets with the Dzyaloshinskii–Moriya (DM) interaction, characterized by a topological number. We study the profile of an axially symmetric skyrmion and give exact formulae for the solution of the corresponding far-field and near-field equations, in the asymptotic limit of small DM parameter (alternatively

    更新日期:2020-05-28
  • Nonadditive topological pressure for flows
    Nonlinearity (IF 1.505) Pub Date : 2020-05-28
    Luis Barreira and Carllos Holanda

    We introduce a version of the nonadditive topological pressure for flows and we describe some of its main properties. In particular, we discuss how the nonadditive topological pressure varies with the data and we establish a variational principle in terms of the Kolmogorov–Sinai entropy. We also consider corresponding capacity topological pressures. In the particular case of subadditive families of

    更新日期:2020-05-28
  • Existence of a solution to the stochastic nonlocal Cahn–Hilliard Navier–Stokes model via a splitting-up method
    Nonlinearity (IF 1.505) Pub Date : 2020-05-28
    G Deugoué, B Jidjou Moghomye and T Tachim Medjo

    We consider a stochastic diffuse interface model which describes the motion of an incompressible isothermal mixture of two immiscible fluids under the influence of stochastic external forces in a bounded domain of ##IMG## [http://ej.iop.org/images/0951-7715/33/7/3424/nonab8020ieqn1.gif] {${\mathbb{R}}^{d}$} , d = 2, 3. The model consists of the stochastic Navier–Stokes equations coupled with a nonlocal

    更新日期:2020-05-28
  • Equilibrium states for certain partially hyperbolic attractors
    Nonlinearity (IF 1.505) Pub Date : 2020-05-28
    Todd Fisher and Krerley Oliveira

    We prove that a class of partially hyperbolic attractors introduced by Castro and Nascimento have unique equilibrium states for natural classes of potentials. We also show if the attractors are C 2 and have invariant stable and centre-unstable foliations, then there is a unique equilibrium state for the geometric potential and its 1-parameter family. We do this by applying general techniques developed

    更新日期:2020-05-28
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