• Nonlinearity (IF 1.505) Pub Date : 2020-10-11
Klaudiusz Czudek

We consider systems of two specific piecewise linear homeomorphisms of the unit interval, so called Alsedà–Misiurewicz systems, and investigate the basic properties of Markov chains which arise when these two transformations are applied randomly with probabilities depending on the point of the interval. Though this iterated function system is not contracting in average and known methods do not apply

更新日期：2020-10-12
• Nonlinearity (IF 1.505) Pub Date : 2020-10-11
Ji-hua Ma and Yan-fang Zhang

We calculate topological Hausdorff dimensions of a class of fractal squares by constructing certain self-similar curves. Examples include some generalized Sierpiński carpets, which have the same Hausdorff dimensions but different topological Hausdorff dimensions. Applications are given to the study of Lipschitz equivalence of fractal squares.

更新日期：2020-10-12
• Nonlinearity (IF 1.505) Pub Date : 2020-10-08
Ricardo F Ferreira, Sandro Gallo and Frédéric Paccaut

It is well-known that there always exists at least one stationary measure compatible with a continuous g -function g . Here we prove that if the set of discontinuities of a g -function g has null measure under a candidate measure obtained by some asymptotic procedure, then this candidate measure is compatible with g . We explore several implications of this result, and discuss comparisons with the

更新日期：2020-10-12
• Nonlinearity (IF 1.505) Pub Date : 2020-10-07
Harry Crimmins and Gary Froyland

We study the stability of statistical properties of Anosov maps on tori by examining the stability of the spectrum of an analytically twisted Perron–Frobenius operator on the anisotropic Banach spaces of Gouëzel and Liverani (2006 Ergod. Theor. Dyn. Syst. 26 189–217). By extending our previous work in Crimmins and Froyland (2019 Ann. Henri Poincaré 20 3113–3161), we obtain the stability of various

更新日期：2020-10-08
• Nonlinearity (IF 1.505) Pub Date : 2020-10-07
Martin Friesen and Oleksandr Kutoviy

A variant of the abstract Cauchy–Kovalevskaya theorem is considered. We prove existence and uniqueness of classical solutions to the nonlinear, non-autonomous initial value problem ##IMG## [http://ej.iop.org/images/0951-7715/33/11/6134/nonab9dc9ieqn1.gif] {$\frac{\mathrm{d}u\left(t\right)}{\mathrm{d}t}=A\left(t\right)u\left(t\right)+B\left(u\left(t\right),t\right),\enspace u\left(0\right)=x$} in a

更新日期：2020-10-08
• Nonlinearity (IF 1.505) Pub Date : 2020-10-07
Michael Burr and Christian Wolf

We investigate the computability of thermodynamic invariants at zero temperature for one-dimensional subshifts of finite type. In particular, we prove that the residual entropy (i.e., the joint ground state entropy) is an upper semi-computable function on the space of continuous potentials, but it is not computable. Next, we consider locally constant potentials for which the zero-temperature measure

更新日期：2020-10-08
• Nonlinearity (IF 1.505) Pub Date : 2020-10-07
Yu Deng and Christian Zillinger

We consider the effects of mixing by smooth bilipschitz shear flows in the linearized Euler equations on ##IMG## [http://ej.iop.org/images/0951-7715/33/11/6176/nonaba236ieqn1.gif] {${\mathbb{T}}_{L}{\times}\mathbb{R}$} . Here, we construct a model which is closely related to a small high frequency perturbation around Couette flow, which exhibits linear inviscid damping for L sufficiently small, but

更新日期：2020-10-08
• Nonlinearity (IF 1.505) Pub Date : 2020-10-07
Wen Si and Yingfei Yi

We consider the existence of responsive tori for the completely degenerate Hamiltonian system with the following Hamiltonian ##IMG## [http://ej.iop.org/images/0951-7715/33/11/6072/nonaba093ieqn1.gif] {$H\left(\theta ,I,x,y,{\epsilon}\right)=\langle \omega ,I\rangle +\lambda \frac{{x}^{n}}{n}+\frac{{y}^{m}}{m}+{\epsilon}P\left(\theta ,x,y,{\epsilon}\right),\enspace \left(\theta ,I,x,y\right)\in {\m 更新日期：2020-10-08 • Nonlinearity (IF 1.505) Pub Date : 2020-10-07 Jason Murphy and Yanzhi Zhang We carry out numerical simulations of the defocusing energy-supercritical nonlinear wave equation for a range of spherically-symmetric initial conditions. We demonstrate numerically that the critical Sobolev norm of solutions remains bounded in time. This lends support to conditional scattering results that have been recently established for nonlinear wave equations. 更新日期：2020-10-08 • Nonlinearity (IF 1.505) Pub Date : 2020-10-07 Hang Ding and Jun Zhou In this paper, we revisit the following nonlocal Kirchhoff diffusion problem:∂tu+M([u]s2)LKu=|u|p−2u,inΩ×R+,u(x,t)=0,in(RN\Ω)×R+,u(x,0)=u0(x),inΩ,where ##IMG## [http://ej.iop.org/images/0951-7715/33/11/6099/nonab9f84ieqn2.gif] {${\Omega}\subset {\mathbb{R}}^{N}$} is a bounded domain with Lipschitz boundary, [ u ] s is the Gagliardo seminorm of u , 0 < s < min{1, N /2}, ##IMG## [http://ej.iop.org/i 更新日期：2020-10-08 • Nonlinearity (IF 1.505) Pub Date : 2020-10-06 Pietro Miraglio and Enrico Valdinoci We consider a Dirichlet to Neumann operator ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5997/nonab9dcbieqn1.gif] {${\mathcal{L}}_{a}$} arising in a model for water waves, with a nonlocal parameter a ∈ (−1, 1). We deduce the expression of the operator in terms of the Fourier transform, highlighting a local behaviour for small frequencies and a nonlocal behaviour for large frequencies. We further 更新日期：2020-10-07 • Nonlinearity (IF 1.505) Pub Date : 2020-10-06 Ludwik Jaksztas Let d ( ɛ ) and ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5919/nonab9a1aieqn1.gif] {$\mathcal{D}\left(\delta \right)$} denote the Hausdorff dimension of the Julia sets of the polynomials p ɛ ( z ) = z 2 + 1/4 + ɛ and f δ ( z ) = (1 + δ ) z + z 2 respectively. In this paper we will study the directional derivative of the functions d ( ɛ ) and ##IMG## [http://ej.iop.org/images/0951-7715/33/1 更新日期：2020-10-07 • Nonlinearity (IF 1.505) Pub Date : 2020-10-06 Andrew N W Hone and Joe Pallister A recurrence relation is said to have the Laurent property if all of its iterates are Laurent polynomials in the initial values with integer coefficients. Recurrences with this property appear in diverse areas of mathematics and physics, ranging from Lie theory and supersymmetric gauge theories to Teichmüller theory and dimer models. In many cases where such recurrences appear, there is a common structural 更新日期：2020-10-07 • Nonlinearity (IF 1.505) Pub Date : 2020-10-04 Jianfeng Lu and Stefan Steinerberger We study synchronization properties of systems of Kuramoto oscillators. The problem can also be understood as a question about the properties of an energy landscape created by a graph. More formally, let G = ( V , E ) be a connected graph and ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5905/nonab9baaieqn1.gif] {${\left({a}_{ij}\right)}_{i,j=1}^{n}$} denotes its adjacency matrix. Let the function 更新日期：2020-10-05 • Nonlinearity (IF 1.505) Pub Date : 2020-10-04 Tao Li, Hebai Chen and Xingwu Chen Continuing the investigation for the number of crossing periodic orbits of nonsmooth Liénard systems in (2008 Nonlinearity 21 2121–42) for the case of a unique equilibrium, in this paper we allow the considered system to have one or multiple equilibria. By constructing two control functions that are decreasing in a much narrower interval than the one used in the above work in the estimate of divergence 更新日期：2020-10-05 • Nonlinearity (IF 1.505) Pub Date : 2020-10-04 Tommaso Lorenzi and Camille Pouchol We study the long-time behaviour of phenotype-structured models describing the evolutionary dynamics of asexual populations whose phenotypic fitness landscape is characterised by multiple peaks. First we consider the case where phenotypic changes do not occur, and then we include the effect of heritable phenotypic changes. In the former case the model is formulated as an integrodifferential equation 更新日期：2020-10-05 • Nonlinearity (IF 1.505) Pub Date : 2020-09-30 Farrukh Mukhamedov, Otabek Khakimov and Ahmad Fadillah Embong In the present paper, we are aiming to study limiting behaviour of infinite dimensional Volterra operators. We introduce two classes ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5875/nonab9a1cieqn1.gif] {${\tilde {\mathcal{V}}}^{+}$} and ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5875/nonab9a1cieqn2.gif] {${\tilde {\mathcal{V}}}^{-}$} of infinite dimensional Volterra operators. For operators 更新日期：2020-10-02 • Nonlinearity (IF 1.505) Pub Date : 2020-09-30 Hiroki Takahasi We give exponential upper bounds on the probability with which the denominator of the n th convergent in the regular continued fraction expansion stays away from the mean ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5861/nonab9a1dieqn1.gif] {$\frac{n{\pi }^{2}}{12\enspace \mathrm{log}\enspace 2}$} . The exponential rate is best possible, given by an analytic function related to the dimension spectrum 更新日期：2020-10-02 • Nonlinearity (IF 1.505) Pub Date : 2020-09-30 Pablo Amster, Gonzalo Robledo and Daniel Sepúlveda This paper introduces a new consideration in the well known chemostat model of a one-species with a periodic input of single nutrient with period ω , which is described by a system of differential delay equations. The delay represents the interval time between the consumption of nutrient and its metabolization by the microbial species. We obtain a necessary and sufficient condition ensuring the existence 更新日期：2020-10-02 • Nonlinearity (IF 1.505) Pub Date : 2020-09-29 Elisenda Feliu, Alan D Rendall and Carsten Wiuf The multiple futile cycle is a phosphorylation system in which a molecular substrate might be phosphorylated sequentially n times by means of an enzymatic mechanism. The system has been studied mathematically using reaction network theory and ordinary differential equations. It is known that the system might have at least as many as ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5629/nonab9a1eieqn1 更新日期：2020-09-30 • Nonlinearity (IF 1.505) Pub Date : 2020-09-29 Jason Duvall We study a class of nonuniformly expanding interval maps with a neutral fixed point at 0, a class that includes Manneville–Pomeau maps. We prove that the set of points whose forward orbits miss an interval with left endpoint 0 is strong winning for Schmidt’s game. Strong winning sets are dense, have full Hausdorff dimension, and satisfy a countable intersection property. Similar results were known 更新日期：2020-09-30 • Nonlinearity (IF 1.505) Pub Date : 2020-09-29 Julian Fischer and Michael Kniely In the computation of the material properties of random alloys, the method of ‘special quasirandom structures’ attempts to approximate the properties of the alloy on a finite volume with higher accuracy by replicating certain statistics of the random atomic lattice in the finite volume as accurately as possible. In the present work, we provide a rigorous justification for a variant of this method in 更新日期：2020-09-30 • Nonlinearity (IF 1.505) Pub Date : 2020-09-29 Piotr Kalita and Grzegorz Łukaszewicz We consider the Rayleigh–Bénard problem for the three-dimensional Boussinesq system for the micropolar fluid. We introduce the notion of the multivalued eventual semiflow and prove the existence of the two-space global attractor ##IMG## [http://ej.iop.org/images/0951-7715/33/11/5686/nonab9729ieqn1.gif] {${\mathcal{A}}^{K}$} corresponding to weak solutions, for every micropolar parameter K ⩾ 0 denoting 更新日期：2020-09-30 • Nonlinearity (IF 1.505) Pub Date : 2020-09-29 J Slipantschuk, M Richter, D J Chappell, G Tanner, W Just and O F Bandtlow The computation of wave-energy distributions in the mid-to-high frequency regime can be reduced to ray-tracing calculations. Solving the ray-tracing problem in terms of an operator equation for the energy density leads to an inhomogeneous equation which involves a Perron–Frobenius operator defined on a suitable Sobolev space. Even for fairly simple geometries, let alone realistic scenarios such as 更新日期：2020-09-30 • Nonlinearity (IF 1.505) Pub Date : 2020-09-29 Elena Beretta, Cecilia Cavaterra and Luca Ratti In this paper we consider the monodomain model of cardiac electrophysiology. After an analysis of the well-posedness of the model we determine an asymptotic expansion of the perturbed potential due to the presence of small conductivity inhomogeneities (modelling small ischemic regions in the cardiac tissue) and use it to detect the anomalies from partial boundary measurements. This is done by determining 更新日期：2020-09-30 • Nonlinearity (IF 1.505) Pub Date : 2020-09-21 Sergey Gavrilyuk, Boniface Nkonga, Keh-Ming Shyue and Lev Truskinovsky We show that, contrary to popular belief, lower order dispersive regularization of hyperbolic systems does not exclude the development of the localized shock-like transition fronts. To guide the numerical search of such solutions, we generalize Rankine–Hugoniot relations to cover the case of higher order dispersive discontinuities and study their properties in an idealized case of a transition between 更新日期：2020-09-22 • Nonlinearity (IF 1.505) Pub Date : 2020-09-17 Andrey Piatnitski and Mariya Ptashnyk In this paper homogenization of a mathematical model for biomechanics of a plant tissue with randomly distributed cells is considered. Mechanical properties of a plant tissue are modelled by a strongly coupled system of reaction-diffusion-convection equations for chemical processes in plant cells and cell walls, the equations of poroelasticity for elastic deformations of plant cell walls and middle 更新日期：2020-09-20 • Nonlinearity (IF 1.505) Pub Date : 2020-09-17 Marc Kesseböhmer and Tanja I Schindler On a measure theoretical dynamical system with spectral gap property we consider non-integrable observables with regularly varying tails. Under a mild mixing condition we show that the appropriately normed and trimmed sum process of these observables then converges in mean. This result is new also for the special case of i.i.d. random variables and contrasts the general case where mean convergence 更新日期：2020-09-20 • Nonlinearity (IF 1.505) Pub Date : 2020-09-15 Mihaela Ifrim and Daniel Tataru A fundamental question in the study of water waves is the existence and stability of solitary waves. Solitary waves have been proved to exist and have been studied in many interesting situations, and often arise from the balance of different forces/factors influencing the fluid dynamics, e.g. gravity, surface tension or the fluid bottom. However, the existence of solitary waves has remained an open 更新日期：2020-09-16 • Nonlinearity (IF 1.505) Pub Date : 2020-09-15 A Alexandrou Himonas and Dionyssios Mantzavinos The initial-boundary value problem (ibvp) for the nonlinear Schrödinger (NLS) equation on the half-plane with nonzero boundary data is studied by advancing a novel approach recently developed for the well-posedness of the cubic NLS equation on the half-line, which takes advantage of the solution formula produced via the unified transform of Fokas for the associated linear ibvp. For initial data in 更新日期：2020-09-16 • Nonlinearity (IF 1.505) Pub Date : 2020-09-03 François Gay-Balmaz and Cesare Tronci This paper extends the Madelung–Bohm formulation of quantum mechanics to describe the time-reversible interaction of classical and quantum systems. The symplectic geometry of the Madelung transform leads to identifying hybrid quantum–classical Lagrangian paths extending the Bohmian trajectories from standard quantum theory. As the classical symplectic form is no longer preserved, the nontrivial evolution 更新日期：2020-09-05 • Nonlinearity (IF 1.505) Pub Date : 2020-09-03 Dieter Bothe We consider the initial value problem ##IMG## [http://ej.iop.org/images/0951-7715/33/10/5425/nonab987dieqn1.gif] {$\dot {x}\left(t\right)=v\left(t,x\left(t\right)\right)\;\text{for}\,\;t\in \left(a,b\right),x\left({t}_{0}\right)={x}_{0}} which determines the pathlines of a two-phase flow, i.e. v = v ( t , x ) is a given velocity field of the type ##IMG## [http://ej.iop.org/images/0951-7715/33/10/5425/nonab987dieqn2 更新日期：2020-09-05 • Nonlinearity (IF 1.505) Pub Date : 2020-09-03 Felipe Pérez Pereira We study the Hausdorff dimension of Gibbs measures with infinite entropy with respect to maps of the interval with countably many branches. We show that under simple conditions, such measures are symbolic-exact dimensional, and provide an almost sure value for the symbolic dimension. We also show that the lower local dimension dimension is almost surely equal to zero, while the upper local dimension 更新日期：2020-09-05 • Nonlinearity (IF 1.505) Pub Date : 2020-09-03 Chunrong Feng, Baoyou Qu and Huaizhong Zhao This paper contains two parts. In the first part, we study the ergodicity of periodic measures of random dynamical systems on a separable Banach space. We obtain that the periodic measure of the continuous time skew-product dynamical system generated by a random periodic path is ergodic if and only if the underlying noise metric dynamical system at discrete time of integral multiples of the period 更新日期：2020-09-05 • Nonlinearity (IF 1.505) Pub Date : 2020-09-02 David N Reynolds and Roman Shvydkoy In this paper we address the problem of well-posedness of multi-dimensional topological Euler-alignment models introduced by Roman and Tadmor (2018 arXiv:1806.01371). The main result demonstrates local existence and uniqueness of classical solutions in class ( ρ , u ) ∈ H m + α × H m +1 on the periodic domain ##IMG## [http://ej.iop.org/images/0951-7715/33/10/5176/nonab9497ieqn1.gif] {{\mathbb{T}}^{n}$} 更新日期：2020-09-03 • Nonlinearity (IF 1.505) Pub Date : 2020-09-02 Evan Miller In this paper, we will prove a new result that guarantees the global existence of solutions to the Navier–Stokes equation in three dimensions when the initial data is sufficiently close to being two dimensional. This result interpolates between the global existence of smooth solutions for the two dimensional Navier–Stokes equation with arbitrarily large initial data, and the global existence of smooth 更新日期：2020-09-03 • Nonlinearity (IF 1.505) Pub Date : 2020-09-02 K Rajaratnam and I M Sigal We consider the non-relativistic Chern–Simons equations proposed by Zhang, Hansen and Kivelson as the mean field theory of the fractional Hall effect. We prove the existence of the vortex lattice solutions (i.e. solution with lattice symmetry and with topological degree one per lattice cell) similar to the Abrikosov solutions of superconductivity. We derive an asymptotic expression for the energy per 更新日期：2020-09-03 • Nonlinearity (IF 1.505) Pub Date : 2020-09-02 A Its and V Sukhanov This paper is the first part of our study the asymptotic behavior of the solutions of the cylindrical Korteweg–de Vries equation (cKdV). In this first part, we consider the solutions from Schwarz’s class and calculate the large time asymptotics using the method based on the asymptotic solution of the associated direct scattering problem. This approach was first suggested, in the cases of usual KdV 更新日期：2020-09-03 • Nonlinearity (IF 1.505) Pub Date : 2020-08-26 Yusuke Doi and Kazuyuki Yoshimura We construct a nonlinear lattice that has a particular symmetry in its potential function consisting of long-range pairwise interactions. The symmetry enhances smooth propagation of discrete breathers, and it is defined by an invariance of the potential function with respect to a map acting on the complex normal mode coordinates. Condition of the symmetry is given by a set of algebraic equations with 更新日期：2020-08-27 • Nonlinearity (IF 1.505) Pub Date : 2020-08-26 Chiun-Chang Lee, Zhi-An Wang and Wen Yang This paper is concerned with the stationary problem of an aero-taxis system with physical boundary conditions proposed by Tuval et al (2005 Proc. Natl Acad. Sci . 102 2277–82) to describe the boundary layer formation in the air–fluid interface in any dimensions. By considering a special case where fluid is free, the stationary problem is essentially reduced to a singularly perturbed nonlocal semi-linear 更新日期：2020-08-27 • Nonlinearity (IF 1.505) Pub Date : 2020-08-23 Chunhua Jin In this paper, we deal with the Chaplain–Lolas’s model of cancer invasion with tissue remodelling ##IMG## [http://ej.iop.org/images/0951-7715/33/10/5049/nonab9249ieqn1.gif] {$\left\{\begin{aligned}\hfill & {u}_{t}={\Delta}u-\chi \mathbf{\nabla }\cdot \left(u\mathbf{\nabla }v\right)-\xi \mathbf{\nabla }\cdot \left(u\mathbf{\nabla }w\right)+\mu u\left(1-u\right)+\beta uv,\hfill \\ \hfill & {v}_{t}=D{\Delta}v+u-uv

更新日期：2020-08-24
• Nonlinearity (IF 1.505) Pub Date : 2020-08-23
Michael Winkler

The Cauchy problem in ##IMG## [http://ej.iop.org/images/0951-7715/33/10/5007/nonab9247ieqn1.gif] {${\mathbb{R}}^{n}$} for the Keller–Segel system ##IMG## [http://ej.iop.org/images/0951-7715/33/10/5007/nonab9247ieqn2.gif] {$\begin{cases}_{t}={\Delta}u-\nabla \cdot \left(u\nabla v\right),\quad \hfill \\ {v}_{t}={\Delta}v-v+u,\quad \hfill \end{cases}$} is considered for n ⩾ 3. Using a basic theory of

更新日期：2020-08-24
• Nonlinearity (IF 1.505) Pub Date : 2020-08-23
Chueh-Hsin Chang, Chiun-Chuan Chen, Li-Chang Hung, Masayasu Mimura and Toshiyuki Ogawa

This paper considers the problem: if coexistence occurs in the long run when a third species w invades an ecosystem consisting of two species u and v on ##IMG## [http://ej.iop.org/images/0951-7715/33/10/5080/nonab9244ieqn1.gif] {$\mathbb{R}$} , where u , v and w compete with one another. Under the assumption that the influence of w on u and v is small and other suitable conditions, we show that the

更新日期：2020-08-24
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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] {${f}_{\beta 更新日期：2020-07-23 • Nonlinearity (IF 1.505) Pub Date : 2020-07-22 Francesco Boarotto, Roberto Monti and Francesco Palmurella This paper is devoted to a third order study of the end-point map in sub-Riemannian geometry. We first prove third order open mapping results for maps from a Banach space into a finite dimensional manifold. In a second step, we compute the third order term in the Taylor expansion of the end-point map and we specialize the abstract theory to the study of length-minimality of sub-Riemannian strictly 更新日期：2020-07-23 • Nonlinearity (IF 1.505) Pub Date : 2020-07-22 Claudianor O Alves and Abbas Moameni In this paper, by making use of a new variational principle, we prove existence of nontrivial solutions for two different types of semilinear problems with Neumann boundary conditions in unbounded domains. Namely, we study elliptic equations and Hamiltonian systems on the unbounded domain ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4568/nonab8bacieqn1.gif] {${\Omega}={\mathbb{R}}^{m}{\times}{B}_{r}$} 更新日期：2020-07-23 • 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
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