-
Finite-time blow-up in hyperbolic Keller–Segel system of consumption type with logarithmic sensitivity Nonlinearity (IF 1.7) Pub Date : 2024-02-28 Jungkyoung Na
This paper deals with finite-time blow-up of a hyperbolic Keller–Segel system of consumption type with the logarithmic sensitivity 0\right)$?> ∂tρ=−χ∇⋅ρ∇logc,∂tc=−μcρχ,μ>0 in Rd(d⩾1) for nonvanishing initial data. This system is closely related to tumor angiogenesis, an important example of chemotaxis. Our singularity formation is not because c touches zero (which makes logc diverge) but due to the
-
On uniqueness properties of solutions of the generalized fourth-order Schrödinger equations Nonlinearity (IF 1.7) Pub Date : 2024-02-27 Zachary Lee, Xueying Yu
In this paper, we study uniqueness properties of solutions to the generalized fourth-order Schrödinger equations in any dimension d of the following forms, i∂tu+∑j=1d∂xj4u=Vt,xu,andi∂tu+∑j=1d∂xj4u+Fu,u‾=0. We show that a linear solution u with fast enough decay in certain Sobolev spaces at two different times has to be trivial. Consequently, if the difference between two nonlinear solutions u 1 and
-
Collapse dynamics for two-dimensional space-time nonlocal nonlinear Schrödinger equations Nonlinearity (IF 1.7) Pub Date : 2024-02-21 Justin T Cole, Abdullah M Aurko, Ziad H Musslimani
The question of collapse (blow-up) in finite time is investigated for the two-dimensional (non-integrable) space-time nonlocal nonlinear Schrödinger equations. Starting from the two-dimensional extension of the well known AKNS q,r system, three different cases are considered: (i) partial and full parity-time (PT) symmetric, (ii) reverse-time (RT) symmetric, and (iii) general q,r system. Through extensive
-
Monotonic convergence of positive radial solutions for general quasilinear elliptic systems Nonlinearity (IF 1.7) Pub Date : 2024-02-20 Daniel Devine, Paschalis Karageorgis
We study the asymptotic behavior of positive radial solutions for quasilinear elliptic systems that have the form Δpu=c1|x|m1⋅g1v⋅|∇u|αin Rn,Δpv=c2|x|m2⋅g2v⋅g3|∇u|in Rn, where Δp denotes the p-Laplace operator, p > 1, n⩾2 , c1,c2>0 and m1,m2,α⩾0 . For a general class of functions gj which grow polynomially, we show that every non-constant positive radial solution (u, v) asymptotically approaches (u0
-
A regularity result for the free boundary compressible Euler equations of a liquid Nonlinearity (IF 1.7) Pub Date : 2024-02-19 Linfeng Li
We derive a priori estimates for the compressible free boundary Euler equations in the case of a liquid without surface tension. We provide a new weighted functional framework which leads to the improved regularity of the flow map by using the Hardy inequality. One of main ideas is to decompose the initial density function. It is worth mentioning that in our analysis we do not need the higher order
-
Exponential rate of decay of correlations of equilibrium states associated with non-uniformly expanding circle maps Nonlinearity (IF 1.7) Pub Date : 2024-02-19 Eduardo Garibaldi, Irene Inoquio-Renteria
In the context of expanding maps of the circle with an indifferent fixed point, understanding the joint behavior of dynamics and pairs of moduli of continuity (ω,Ω) may be a useful element for the development of equilibrium theory. Here we identify a particular feature of modulus Ω (precisely limx→0+supdΩ(dx)/Ω(d)=0 ) as a sufficient condition for the system to exhibit exponential decay of correlations
-
Bounds on buoyancy driven flows with Navier-slip conditions on rough boundaries Nonlinearity (IF 1.7) Pub Date : 2024-02-15 Fabian Bleitner, Camilla Nobili
We consider two-dimensional Rayleigh–Bénard convection with Navier-slip and fixed temperature boundary conditions at the two horizontal rough walls described by the height function h. We prove rigorous upper bounds on the Nusselt number Nu which capture the dependence on the curvature of the boundary κ and the (non-constant) friction coefficient α explicitly. If h∈W2,∞ and κ satisfies a smallness condition
-
Modeling the interplay of oscillatory synchronization and aggregation via cell–cell adhesion Nonlinearity (IF 1.7) Pub Date : 2024-02-13 Tilmann Glimm, Daniel Gruszka
We present a model of systems of cells with intracellular oscillators (‘clocks’). This is motivated by examples from developmental biology and from the behavior of organisms on the threshold to multicellularity. Cells undergo random motion and adhere to each other. The adhesion strength between neighbors depends on their clock phases in addition to a constant baseline strength. The oscillators are
-
Revisiting the Kepler problem with linear drag using the blowup method and normal form theory Nonlinearity (IF 1.7) Pub Date : 2024-02-09 K Uldall Kristiansen
In this paper, we revisit the Kepler problem with linear drag. With dissipation, the energy and the angular momentum are both decreasing, but in Margheri et al (2017 Celest. Mech. Dyn. Astron. 127 35–48) it was shown that the eccentricity vector has a well-defined limit in the case of linear drag. This limiting eccentricity vector defines a conserved quantity, and in the present paper, we prove that
-
Dihedral rings of patterns emerging from a Turing bifurcation Nonlinearity (IF 1.7) Pub Date : 2024-02-09 Dan J Hill, Jason J Bramburger, David J B Lloyd
Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is known numerically or analytically about their formation when the patterns are strongly interacting. We prove that approximate strongly interacting patterns can emerge in various ring-like dihedral configurations, bifurcating
-
Higgs fields, non-abelian Cauchy kernels and the Goldman symplectic structure Nonlinearity (IF 1.7) Pub Date : 2024-02-07 M Bertola, C Norton, G Ruzza
We consider the moduli space of vector bundles of rank n and degree ng over a fixed Riemann surface of genus g⩾2 with the explicit parametrization in terms of the Tyurin data. The ‘non-abelian’ theta divisor consists of bundles such that h1⩾1 . On the complement of this divisor we construct a non-abelian (i.e. matrix) Cauchy kernel explicitly in terms of the Tyurin data. With the additional datum of
-
Strong convergence of the vorticity and conservation of the energy for the α-Euler equations Nonlinearity (IF 1.7) Pub Date : 2024-02-06 Stefano Abbate, Gianluca Crippa, Stefano Spirito
In this paper, we study the convergence of solutions of the α-Euler equations to solutions of the Euler equations on the two-dimensional torus. In particular, given an initial vorticity ω 0 in Lxp for p∈(1,∞) , we prove strong convergence in Lt∞Lxp of the vorticities q α , solutions of the α-Euler equations, towards a Lagrangian and energy-conserving solution of the Euler equations. Furthermore, if
-
Bifurcation and regularity analysis of the Schrödinger-Poisson equation Nonlinearity (IF 1.7) Pub Date : 2024-02-05 Patrizia Pucci, Linlin Wang, Binlin Zhang
The aim of this paper is to present bifurcation results for (weak) solutions of the Schrödinger-Poisson system in R3 , involving subcritical and critical nonlinearities and using the global bifurcation theorem. Furthermore, we establish the existence of unbounded components of (weak) solutions, which bifurcate from trivial solutions and from infinity, respectively. The novelties of the paper lie in
-
Quasi-periodic waves to the defocusing nonlinear Schrödinger equation Nonlinearity (IF 1.7) Pub Date : 2024-02-02 Ying-Nan Zhang, Xing-Biao Hu, Jian-Qing Sun
A direct approach for the quasi-periodic wave solutions to the defocusing nonlinear Schrödinger equation is proposed based on the theta functions and Hirota’s bilinear method. We transform the problem into a system of algebraic equations, which can be formulated into a least squares problem and then solved by using numerical iterative methods. A rigorous asymptotic analysis demonstrates that these
-
Boundary asymptotics of non-intersecting Brownian motions: Pearcey, Airy and a transition Nonlinearity (IF 1.7) Pub Date : 2024-01-30 Thorsten Neuschel, Martin Venker
We study n non-intersecting Brownian motions, corresponding to the eigenvalues of an n × n Hermitian Brownian motion. At the boundary of their limit shape we find that only three universal processes can arise: the Pearcey process close to merging points, the Airy line ensemble at edges and a novel determinantal process describing the transition from the Pearcey process to the Airy line ensemble. The
-
Backpropagation in hyperbolic chaos via adjoint shadowing Nonlinearity (IF 1.7) Pub Date : 2024-01-30 Angxiu Ni
To generalise the backpropagation method to both discrete-time and continuous-time hyperbolic chaos, we introduce the adjoint shadowing operator S acting on covector fields. We show that S can be equivalently defined as: S is the adjoint of the linear shadowing operator S; S is given by a ‘split then propagate’ expansion formula; S(ω) is the only bounded inhomogeneous adjoint solution of ω.By (a),
-
New Liouville type theorems for the stationary Navier–Stokes, MHD, and Hall–MHD equations Nonlinearity (IF 1.7) Pub Date : 2024-01-30 Youseung Cho, Jiří Neustupa, Minsuk Yang
We establish new Liouville-type theorems for weak solutions of the stationary Navier–Stokes equations, stationary magnetohydrodynamics (MHD) equations and stationary Hall–MHD equations under some conditions on the growth of certain Lebesgue norms of the velocity and the magnetic field.
-
Tit-for-tat dynamics and market volatility Nonlinearity (IF 1.7) Pub Date : 2024-01-29 Simina Brânzei
We consider tit-for-tat dynamics in production markets, where there is a set of n players connected via a weighted graph. Each player i can produce an eponymous good using its linear production function, given as input various amounts of goods in the system. In the tit-for-tat dynamic, each player i shares its good with its neighbours in fractions proportional to how much they helped player i’s production
-
Glimm’s method and density of wild data for the Euler system of gas dynamics * Nonlinearity (IF 1.7) Pub Date : 2024-01-24 Elisabetta Chiodaroli, Eduard Feireisl
We adapt Glimm’s approximation method to the framework of convex integration to show density of wild data for the (complete) Euler system of gas dynamics. The desired infinite family of entropy admissible solutions emanating from the same initial data is obtained via convex integration of suitable Riemann problems pasted with local smooth solutions. In addition, the wild data belong to BV class.
-
Hardy inequalities for magnetic p-Laplacians Nonlinearity (IF 1.7) Pub Date : 2024-01-23 Cristian Cazacu, David Krejčiřík, Nguyen Lam, Ari Laptev
We establish improved Hardy inequalities for the magnetic p-Laplacian due to adding nontrivial magnetic fields. We also prove that for Aharonov–Bohm magnetic fields the sharp constant in the Hardy inequality becomes strictly larger than in the case of a magnetic-free p-Laplacian. We also post some remarks with open problems.
-
Blowup analysis for a quasi-exact 1D model of 3D Euler and Navier–Stokes Nonlinearity (IF 1.7) Pub Date : 2024-01-22 Thomas Y Hou, Yixuan Wang
We study the singularity formation of a quasi-exact 1D model proposed by Hou and Li (2008 Commun. Pure Appl. Math. 61 661–97). This model is based on an approximation of the axisymmetric Navier–Stokes equations in the r direction. The solution of the 1D model can be used to construct an exact solution of the original 3D Euler and Navier–Stokes equations if the initial angular velocity, angular vorticity
-
Uniform regularity and zero capillarity-viscosity limit for an inhomogeneous incompressible fluid model of Korteweg type in half-space Nonlinearity (IF 1.7) Pub Date : 2024-01-22 Fucai Li, Shuxing Zhang, Zhipeng Zhang
In this paper, we study the uniform regularity and zero capillarity-viscosity limit for an inhomogeneous incompressible fluid model of Korteweg type in the half-space R+3 . We consider the Navier-slip boundary condition for velocity and the Dirichlet boundary condition for the gradient of density. By establishing the conormal energy estimates, we prove that there exists a unique strong solution of
-
Upper bounds for the moduli of polynomial-like maps Nonlinearity (IF 1.7) Pub Date : 2024-01-22 Alexander Blokh, Lex Oversteegen, Vladlen Timorin
We establish a version of the Pommerenke–Levin–Yoccoz inequality for the modulus of a polynomial-like (PL) restriction of a polynomial and give two applications. First we show that if the modulus of a PL restriction of a polynomial is bounded from below then this restricts the combinatorics of the polynomial. The second application concerns parameter slices of cubic polynomials given by the non-repelling
-
Structural stability of subsonic steady states to the hydrodynamic model for semiconductors with sonic boundary Nonlinearity (IF 1.7) Pub Date : 2024-01-19 Yue-Hong Feng, Haifeng Hu, Ming Mei
The hydrodynamic model for semiconductors with sonic boundary, represented by Euler–Poisson equations, possesses the various physical steady states including interior-subsonic/interior-supersonic/shock-transonic/C 1-smooth-transonic steady states. Since these physical steady states result in some serious singularities at the sonic boundary (their gradients are infinity), this makes that the structural
-
Normalized ground states for the Sobolev critical Schrödinger equation with at least mass critical growth Nonlinearity (IF 1.7) Pub Date : 2024-01-18 Quanqing Li, Vicenţiu D Rădulescu, Wen Zhang
In the present paper, we investigate the existence of ground state solutions to the Sobolev critical nonlinear Schrödinger equation −Δu+λu=gu+|u|2∗−2u inRN,∫RN|u|2dx=m2, where N⩾3 , m > 0, 2∗:=2NN−2 , λ is an unknown parameter that will appear as a Lagrange multiplier, g is a mass critical or supercritical but Sobolev subcritical nonlinearity. With the aid of the minimization of the energy functional
-
On the generalization of classical Zernike system Nonlinearity (IF 1.7) Pub Date : 2024-01-18 Cezary Gonera, Joanna Gonera, Piotr Kosiński
We generalize the results obtained recently (Blasco et al 2023 Nonlinearity 36 1143) by providing a very simple proof of the superintegrability of the Hamiltonian H=p⃗2+F(q⃗⋅p⃗) , q⃗,p⃗∈R2 , for any analytic function F. The additional integral of motion is constructed explicitly and shown to reduce to a polynomial in canonical variables for polynomial F. The generalization to the case q⃗,p⃗∈Rn is sketched
-
Two-dimensional reductions of the Whitham modulation system for the Kadomtsev–Petviashvili equation Nonlinearity (IF 1.7) Pub Date : 2024-01-18 Gino Biondini, Alexander J Bivolcic, Mark A Hoefer, Antonio Moro
Two-dimensional reductions of the Kadomtsev–Petviashvili(KP)–Whitham system, namely the overdetermined Whitham modulation system for five dependent variables that describe the periodic solutions of the KP equation, are studied and characterized. Three different reductions are considered corresponding to modulations that are independent of x, independent of y, and of t (i.e. stationary), respectively
-
Small Darcy number limit of the Navier–Stokes–Darcy system Nonlinearity (IF 1.7) Pub Date : 2024-01-17 Wenqi Lyu, Xiaoming Wang
We study the small Darcy number behavior of the Navier–Stokes–Darcy system with the conservation of mass, Beavers–Joseph–Saffman–Jones condition, and the Lions balance of the normal-force interface boundary conditions imposed on the interface separating the Navier–Stokes flow and Darcy flow. We show that the asymptotic behavior of the coupled system, at small Darcy number, can be captured by two semi-decoupled
-
Dynamics of the Fermi–Ulam model in an external gravitational field Nonlinearity (IF 1.7) Pub Date : 2024-01-17 Yaqi Liang, Xiong Li
In this paper, we are concerned with the possibility of bounded growth of the energy of the Fermi–Ulam model in an external gravitational field. The boundedness of all orbits is established when the forced oscillation is almost periodic and real analytic with respect to time. Furthermore, the existence of infinitely many bounded orbits will be proved when the forced oscillation is only supposed to
-
Kolmogorov’s dissipation number and determining wavenumber for dyadic models Nonlinearity (IF 1.7) Pub Date : 2024-01-17 Mimi Dai, Margaret Hoeller, Qirui Peng, Xiangxiong Zhang
We study some dyadic models for incompressible magnetohydrodynamics and Navier–Stokes equation. The existence of fixed point and stability of the fixed point are established. The scaling law of Kolmogorov’s dissipation wavenumber arises from heuristic analysis. In addition, a time-dependent determining wavenumber is shown to exist; moreover, the time average of the determining wavenumber is proved
-
Synchronization of Turing patterns in complex networks of reaction–diffusion systems set in distinct domains Nonlinearity (IF 1.7) Pub Date : 2024-01-16 M A Aziz-Alaoui, Guillaume Cantin, Alexandre Thorel
We present an innovative complex network of reaction–diffusion systems set in distinct domains, with boundary couplings. The complex network models the evolution of interacting populations living in a heterogeneous and fragmented habitat, whose biological individuals migrate from one patch to another. In our model, the displacements of individuals are described by mixed boundary couplings, involving
-
Convergence of mechanical balance laws for water waves: from KdV to Euler Nonlinearity (IF 1.7) Pub Date : 2024-01-16 Samer Israwi, Henrik Kalisch, Bashar Khorbatly
This article takes into account the Korteweg–de Vries (KdV) equation as an approximate model of long waves of small amplitude at the free surface with inviscid fluid. It is demonstrated that the mechanical balance quantities, as defined by the solution of the KdV equation, rigorously approximate those in the Euler system within the L∞ space. Furthermore, these approximations are estimated in relation
-
Irrationality exponent and convergence exponent in continued fraction expansions Nonlinearity (IF 1.7) Pub Date : 2024-01-16 Kunkun Song, Xiaoyan Tan, Zhenliang Zhang
Let x∈(0,1) be an irrational number with continued fraction expansion [a1(x),a2(x),⋯,an(x),⋯] . We give the multifractal spectrum of the irrationality exponent and the convergence exponent of x defined by v(x):=sup{v>0:|x−pq|<1qv for infinitely many (q,p)∈ℕ×ℤ} and τx:=infs⩾0:∑n⩾1an−sx<∞ respectively. To be precise, we completely determine the Hausdorff dimension of Eα,v=x∈0,1: τx=α, vx=v for any α⩾0
-
Existence and uniqueness of solutions to the Peierls–Nabarro model in anisotropic media Nonlinearity (IF 1.7) Pub Date : 2024-01-12 Yuan Gao, James M Scott
We study the existence and uniqueness of solutions to the vector field Peierls–Nabarro (PN) model for curved dislocations in a transversely isotropic medium. Under suitable assumptions for the misfit potential on the slip plane, we reduce the 3D PN model to a nonlocal scalar Ginzburg–Landau equation. For a particular range of elastic coefficients, the nonlocal scalar equation with explicit nonlocal
-
Asymptotic study of critical wave fronts for parameter-dependent Born–Infeld models: physically predicted behaviors and new phenomena Nonlinearity (IF 1.7) Pub Date : 2024-01-08 Maurizio Garrione
In this paper, we study some parameter-dependent reaction-diffusion models governed by the Born–Infeld (or Minkowski) operator. In dependence on two parameters a,b>0 , related to the field strength and to the diffusivity, we investigate the limit critical speed for traveling fronts, together with the limit behavior of the associated critical profiles. As the two main results, on the one hand we rigorously
-
Global well-posedness and asymptotic behavior in critical spaces for the compressible Euler system with velocity alignment Nonlinearity (IF 1.7) Pub Date : 2024-01-04 Xiang Bai, Qianyun Miao, Changhui Tan, Liutang Xue
In this paper, we study the Cauchy problem of the compressible Euler system with strongly singular velocity alignment. We prove the existence and uniqueness of global solutions in critical Besov spaces to the considered system with small initial data. The local-in-time solvability is also addressed. Moreover, we show the large-time asymptotic behaviour and optimal decay estimates of the solutions as
-
Cusps in heavy billiards Nonlinearity (IF 1.7) Pub Date : 2024-01-04 Boris Hasselblatt, Ki Yeun Kim, Mark Levi
We consider billiards with cusps and with gravity pulling the particle into the cusp. We discover an adiabatic invariant in this context; it turns out that the invariant is in form almost identical to the Clairaut integral (angular momentum) for surfaces of revolution. We also approximate the bouncing motion of a particle near a cusp by smooth motion governed by a differential equation—which turns
-
Metrical properties of the large products of partial quotients in continued fractions Nonlinearity (IF 1.7) Pub Date : 2024-01-04 Bo Tan, Qing-Long Zhou
The study of products of consecutive partial quotients in the continued fraction arises naturally out of the improvements to Dirichlet’s theorem. We study the distribution of the two large products of partial quotients among the first n terms. More precisely, writing [a1(x),a2(x),…] the continued fraction expansion of an irrational number x∈(0,1) , for a non-decreasing function φ:N→R , we completely
-
Classification and stability of positive solutions to the NLS equation on the T -metric graph Nonlinearity (IF 1.7) Pub Date : 2024-01-04 Francisco Agostinho, Simão Correia, Hugo Tavares
Given λ > 0 and p > 2, we present a complete classification of the positive H 1-solutions of the equation −u′′+λu=|u|p−2u on the T -metric graph (consisting of two unbounded edges and a terminal edge of length ℓ>0 , all joined together at a single vertex). This study implies, in particular, the uniqueness of action ground states. Moreover, for p∼6− , the notions of action and energy ground states do
-
Global existence and singularity formation for the generalized Constantin–Lax–Majda equation with dissipation: the real line vs. periodic domains Nonlinearity (IF 1.7) Pub Date : 2023-12-29 David M Ambrose, Pavel M Lushnikov, Michael Siegel, Denis A Silantyev
The question of global existence versus finite-time singularity formation is considered for the generalized Constantin–Lax–Majda equation with dissipation −Λσ , where Λσˆ=|k|σ , both for the problem on the circle x∈[−π,π] and the real line. In the periodic geometry, two complementary approaches are used to prove global-in-time existence of solutions for σ⩾1 and all real values of an advection parameter
-
Density of periodic measures and large deviation principle for generalised mod one transformations Nonlinearity (IF 1.7) Pub Date : 2023-12-22 Mao Shinoda, Kenichiro Yamamoto
We introduce a new class of piecewise monotonic maps, called generalised mod one transformations, which include all (α,β) and generalised β -transformations, and prove that all transitive generalised mod one transformations with positive topological entropy satisfy the level-2 large deviation principle with a unique measure of maximal entropy. This is obtained by our result on the density of periodic
-
A diffusive SIS epidemic model with saturated incidence function in a heterogeneous environment * Nonlinearity (IF 1.7) Pub Date : 2023-12-22 Daozhou Gao, Chengxia Lei, Rui Peng, Benben Zhang
In this paper, we propose a diffusive susceptible-infected-susceptible epidemic model in a spatiotemporally heterogeneous environment. We consider a saturated incidence function of the form SIm+S+I , where m is a nonnegative function. When there is a positive disease-induced mortality rate everywhere, we demonstrate that the disease will always become extinct and the susceptible population will stabilize
-
Miura-reciprocal transformations and localizable Poisson pencils Nonlinearity (IF 1.7) Pub Date : 2023-12-22 P Lorenzoni, S Shadrin, R Vitolo
We show that the equivalence classes of deformations of localizable semisimple Poisson pencils of hydrodynamic type with respect to the action of the Miura-reciprocal group contain a local representative and are in one-to-one correspondence with the equivalence classes of deformations of local semisimple Poisson pencils of hydrodynamic type with respect to the action of the Miura group.
-
A road map to the blow-up for a Kirchhoff equation with external force Nonlinearity (IF 1.7) Pub Date : 2023-12-11 Marina Ghisi, Massimo Gobbino
It is well-known that the classical hyperbolic Kirchhoff equation admits infinitely many simple modes, namely time-periodic solutions with only one Fourier component in the space variables. In this paper we assume that, for a suitable choice of the nonlinearity, there exists a heteroclinic connection between two simple modes with different frequencies. Under this assumption, we cook up a forced Kirchhoff
-
Projective integrable mechanical billiards Nonlinearity (IF 1.7) Pub Date : 2023-12-07 Airi Takeuchi, Lei Zhao
In this paper, we use the projective dynamical approach to integrable mechanical billiards as in (Zhao 2021 Commun. Contemp. Math. 24 2150085) to establish the integrability of natural mechanical billiards with the Lagrange problem, which is the superposition of two Kepler problems and a Hooke problem, with the Hooke center at the middle of the Kepler centers, as the underlying mechanical systems,
-
The most probable transition paths of stochastic dynamical systems: a sufficient and necessary characterisation Nonlinearity (IF 1.7) Pub Date : 2023-12-07 Yuanfei Huang, Qiao Huang, Jinqiao Duan
The most probable transition paths (MPTPs) of a stochastic dynamical system are the global minimisers of the Onsager–Machlup action functional and can be described by a necessary but not sufficient condition, the Euler–Lagrange (EL) equation (a second-order differential equation with initial-terminal conditions) from a variational principle. This work is devoted to showing a sufficient and necessary
-
Well–posedness of the three–dimensional NLS equation with sphere–concentrated nonlinearity Nonlinearity (IF 1.7) Pub Date : 2023-12-05 Domenico Finco, Lorenzo Tentarelli, Alessandro Teta
We discuss strong local and global well–posedness for the three–dimensional NLS equation with nonlinearity concentrated on S2 . Precisely, local well–posedness is proved for any C 2 power–nonlinearity, while global well–posedness is obtained either for small data or in the defocusing case under some growth assumptions. With respect to point–concentrated NLS models, widely studied in the literature
-
Blow-up for semilinear parabolic equations in cones of the hyperbolic space Nonlinearity (IF 1.7) Pub Date : 2023-12-05 D D Monticelli, F Punzo
We investigate existence and nonexistence of global in time nonnegative solutions to the semilinear heat equation, with a reaction term of the type eμtup(μ∈R,p>1), posed on cones of the hyperbolic space. Under a certain assumption on µ and p, related to the bottom of the spectrum of −Δ in Hn , we prove that any solution blows up in finite time, for any nontrivial nonnegative initial datum. Instead
-
Canonical curves and Kropina metrics in Lagrangian contact geometry Nonlinearity (IF 1.7) Pub Date : 2023-12-05 Tianyu Ma, Keegan J Flood, Vladimir S Matveev, Vojtěch Žádník
We present a Fefferman-type construction from Lagrangian contact to split-signature conformal structures and examine several related topics. In particular, we describe the canonical curves and their correspondence. We show that chains and null-chains of an integrable Lagrangian contact structure are the projections of null-geodesics of the Fefferman space. Employing the Fermat principle, we realize
-
Invariant measures for a stochastic nonlinear and damped 2D Schrödinger equation Nonlinearity (IF 1.7) Pub Date : 2023-12-05 Zdzisław Brzeźniak, Benedetta Ferrario, Margherita Zanella
We consider a stochastic nonlinear defocusing Schrödinger equation with zero-order linear damping, where the stochastic forcing term is given by a combination of a linear multiplicative noise in the Stratonovich form and a nonlinear noise in the Itô form. We work at the same time on compact Riemannian manifolds without boundary and on relatively compact smooth domains with either the Dirichlet or the
-
The realisation of admissible graphs for coupled vector fields Nonlinearity (IF 1.7) Pub Date : 2023-12-05 Tiago de Albuquerque Amorim, Miriam Manoel
In a coupled network cells can interact in several ways. There is a vast literature from the last 20 years that investigates this interacting dynamics under a graph theory formalism, namely as a graph endowed with an input-equivalence relation on the set of vertices that enables a characterisation of the admissible vector fields that rules the network dynamics. The present work goes in the direction
-
Symmetric periodic orbits in symmetric billiards Nonlinearity (IF 1.7) Pub Date : 2023-12-05 Geraldo César Gonçalves Ferreira, Sylvie Oliffson Kamphorst, Sônia Pinto-de-Carvalho
In this text we study billiards on symmetric ovals and investigate some consequences of the symmetry of the boundary on the dynamics. As it simplifies some calculations, the symmetry helps to obtain the results. We focus on periodic orbits with the same symmetry of the boundary which always exist and prove that typically half of them are elliptic and Moser stable and the other half are hyperbolic with
-
An in-reachability based classification of invariant synchrony patterns in weighted coupled cell networks Nonlinearity (IF 1.7) Pub Date : 2023-12-05 P M Sequeira, J P Hespanha, A P Aguiar
This paper presents an in-reachability based classification of invariant synchrony patterns in coupled cell networks (CCNs). These patterns are encoded through partitions on the set of cells, whose subsets of synchronised cells are called colours. We study the influence of the structure of the network in the qualitative behaviour of invariant synchrony sets, in particular, with respect to the different
-
Spectrality of random convolutions generated by finitely many Hadamard triples Nonlinearity (IF 1.7) Pub Date : 2023-12-05 Wenxia Li, Jun Jie Miao, Zhiqiang Wang
Let {(Nj,Bj,Lj):1⩽j⩽m} be finitely many Hadamard triples in R . Given a sequence of positive integers {nk}k=1∞ and ω=(ωk)k=1∞∈{1,2,…,m}N , let μω,{nk} be the infinite convolution given by μω,nk=δNω1−n1Bω1∗δNω1−n1Nω2−n2Bω2∗⋯∗δNω1−n1Nω2−n2⋯Nωk−nkBωk∗⋯. In order to study the spectrality of μω,{nk} , we first show the spectrality of general infinite convolutions generated by Hadamard triples under the
-
Global solutions to the tangential Peskin problem in 2-D Nonlinearity (IF 1.7) Pub Date : 2023-12-05 Jiajun Tong
We introduce and study the tangential Peskin problem in 2D, which is a scalar drift-diffusion equation with a nonlocal drift. It is derived with a new Eulerian perspective from a special setting of the 2D Peskin problem where an infinitely long and straight 1D elastic string deforms tangentially in the Stokes flow induced by itself in the plane. For initial datum in the energy class satisfying natural
-
Poisson problems involving fractional Hardy operators and measures Nonlinearity (IF 1.7) Pub Date : 2023-11-17 Huyuan Chen, Konstantinos T Gkikas, Phuoc-Tai Nguyen
In this paper, we study the Poisson problem involving a fractional Hardy operator and a measure source. The complex interplay between the nonlocal nature of the operator, the peculiar effect of the singular potential and the measure source induces several new fundamental difficulties in comparison with the local case. To overcome these difficulties, we perform a careful analysis of the dual operator
-
Uniform approximation of 2D Navier-Stokes equations with vorticity creation by stochastic interacting particle systems Nonlinearity (IF 1.7) Pub Date : 2023-11-17 Francesco Grotto, Eliseo Luongo, Mario Maurelli
We consider a stochastic interacting particle system in a bounded domain with reflecting boundary, including creation of new particles on the boundary prescribed by a given source term. We show that such particle system approximates 2D Navier–Stokes equations in vorticity form and impermeable boundary, the creation of particles modeling vorticity creation at the boundary. Kernel smoothing, more specifically
-
Sharp bounds on enstrophy growth for viscous scalar conservation laws Nonlinearity (IF 1.7) Pub Date : 2023-11-16 Dallas Albritton, Nicola De Nitti
We prove sharp bounds on the enstrophy growth in viscous scalar conservation laws. The upper bound is, up to a prefactor, the enstrophy created by the steepest viscous shock admissible by the L∞ and total variation bounds and viscosity. This answers a conjecture by Ayala and Protas (2011 Physica D 240 1553–63), based on numerical evidence, for the viscous Burgers equation.
-
Pulse-adding of temporal dissipative solitons: resonant homoclinic points and the orbit flip of case B with delay Nonlinearity (IF 1.7) Pub Date : 2023-11-15 Andrus Giraldo, Stefan Ruschel
We numerically investigate the branching of temporally localised, two-pulse solutions from one-pulse periodic solutions with non-oscillating tails in delay differential equations (DDEs) with large delay. Solutions of this type are commonly referred to as temporal dissipative solitons (TDSs) (Yanchuk et al 2019 Phys. Rev. Lett. 123 53901) in applications, and we adopt this term here. We show by means
-
Analysis of nonlinear poroviscoelastic flows with discontinuous porosities * Nonlinearity (IF 1.7) Pub Date : 2023-11-13 Markus Bachmayr, Simon Boisserée, Lisa Maria Kreusser
Existence and uniqueness of solutions is shown for a class of viscoelastic flows in porous media with particular attention to problems with nonsmooth porosities. The considered models are formulated in terms of the time-dependent nonlinear interaction between porosity and effective pressure, which in certain cases leads to porosity waves. In particular, conditions for well-posedness in the presence