Journal of Differential Equations最新文献

{"title":"Local exact controllability to the trajectories for the two-dimensional magnetohydrodynamic system with controls acting only on the velocity field","authors":"Qiang Tao ,&nbsp;Zheng-an Yao ,&nbsp;Xuan Yin","doi":"10.1016/j.jde.2025.113237","DOIUrl":"10.1016/j.jde.2025.113237","url":null,"abstract":"<div><div>In this paper, we study the local exact controllability to the trajectories for the two-dimensional incompressible magnetohydrodynamic system on a bounded domain with no-slip boundary condition on the velocity field and the perfect insulating condition on the magnetic field. The controls are distributed in an arbitrarily small nonempty open subset and act only on the velocity field. In this situation, the divergence free condition for the magnetic field can be inherited from the initial value. With this condition, we transform the magnetohydrodynamic system into a coupled system between the Navier-Stokes equations and a scalar equation. Our proof relies on a new Carleman inequality for two kinds of boundary conditions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"433 ","pages":"Article 113237"},"PeriodicalIF":2.4,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global long time uniform well-posedness of 3D incompressible Navier-Stokes equations under time-independent uniqueness condition","authors":"Xinglong Feng ,&nbsp;Yinnian He","doi":"10.1016/j.jde.2025.113254","DOIUrl":"10.1016/j.jde.2025.113254","url":null,"abstract":"<div><div>In this work, inspired by the uniqueness condition of the 3D steady incompressible Navier-Stokes equations, we present a time-independent uniqueness condition depending on <span><math><mo>(</mo><mi>ν</mi><mo>,</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mo>∞</mo></mrow></msub><mo>,</mo><mi>Ω</mi><mo>)</mo></math></span> with <span><math><msub><mrow><mi>f</mi></mrow><mrow><mo>∞</mo></mrow></msub><mo>=</mo><msub><mrow><mi>sup</mi></mrow><mrow><mi>t</mi><mo>≥</mo><mn>0</mn></mrow></msub><mo>⁡</mo><msub><mrow><mo>‖</mo><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>‖</mo></mrow><mrow><mn>0</mn><mo>,</mo><mi>Ω</mi></mrow></msub></math></span> and consider the fully discrete Galerkin method for the 3D time-dependent incompressible Navier-Stokes equations in the infinite time interval <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span>. Furthermore, we provide the long time uniform stability and convergence of the fully discrete Galerkin solution and obtain the global uniform well-posedness (or the existence, uniqueness and long time stability of the solution) of the 3D time-dependent incompressible Navier-Stokes equations under the time-independent uniqueness condition by use of the compact theorem and a new a priori estimate of the fully discrete Galerkin solution.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"436 ","pages":"Article 113254"},"PeriodicalIF":2.4,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On logarithmic double phase problems","authors":"Rakesh Arora ,&nbsp;Ángel Crespo-Blanco ,&nbsp;Patrick Winkert","doi":"10.1016/j.jde.2025.113247","DOIUrl":"10.1016/j.jde.2025.113247","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper we introduce a new logarithmic double phase type operator of the form&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;div&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; whose energy functional is given by&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;↦&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mtext&gt;x&lt;/mtext&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;⊆&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, is a bounded domain with Lipschitz boundary ∂Ω, &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;‾&lt;/mo&gt;&lt;/mover&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; for all &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;‾&lt;/mo&gt;&lt;/mover&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. First, we prove that the logarithmic Musielak-Orlicz Sobolev spaces &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"433 ","pages":"Article 113247"},"PeriodicalIF":2.4,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamics of a periodic predator-prey reaction-diffusion system in heterogeneous environments","authors":"Zhenrui Zhang,&nbsp;Jinfeng Wang","doi":"10.1016/j.jde.2025.113252","DOIUrl":"10.1016/j.jde.2025.113252","url":null,"abstract":"<div><div>This paper is dedicated to investigating a predator-prey reaction-diffusion model with time-periodic, where all coefficient functions are both spatially and temporally heterogeneous. We rigorously characterize the properties of the principal eigenvalue and establish a precise relationship between the coefficient functions and the dynamics. Our results indicate that slow predator movement and short frequency of environmental periodic variations promote successful predator invasion. Conversely, reducing the predator mortality rate facilitates long-term coexistence of both populations. Additionally, we explore the asymptotic behaviors of positive periodic solutions when the diffusion coefficients are large or small, revealing the effects of diffusion on the invasion dynamics.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"435 ","pages":"Article 113252"},"PeriodicalIF":2.4,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143696649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effects of fast diffusion in the logistic equation with refuge","authors":"V.K. Ramos ,&nbsp;C.A. Santos ,&nbsp;A. Suárez","doi":"10.1016/j.jde.2025.113261","DOIUrl":"10.1016/j.jde.2025.113261","url":null,"abstract":"<div><div>This paper studies the behaviour of the positive solution of a logistic equation with respect to a space dependent diffusion rate. The equation also includes a refuge, a zone where the species grows freely. In contrast to the case of homogeneous diffusion coefficient, where the species dies for large diffusion regardless of the birth rate, we show that the species may die, persist or growth indefinitely, depending on the size of the birth rate, for a large increasing of this diffusion rate in a certain region of the space, even more, this growth causes blow up in this region as well as in the refuge.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"436 ","pages":"Article 113261"},"PeriodicalIF":2.4,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143697819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability for inverse potential scattering with attenuation","authors":"Rong Sun ,&nbsp;Ganghua Yuan ,&nbsp;Yue Zhao","doi":"10.1016/j.jde.2025.113259","DOIUrl":"10.1016/j.jde.2025.113259","url":null,"abstract":"<div><div>This paper is concerned with inverse potential scattering problem for Helmholtz equation with constant attenuation. We first derive a logarithmic stability estimate for determining the potential at a single wavenumber by point-source boundary measurements. The proof utilizes the construction of complex geometric optics (CGO) solutions. Further, given the multi-wavenumber data, we derive a stability estimate which consists of two parts: one part is a Lipschitz data discrepancy and the other part is a logarithmic stability. The latter decreases as the wavenumber increases, which exhibits the phenomenon of increasing stability. The proof employs the physical asymptotic behavior of the radiated field and the properties of the Radon transform. Moreover, as multi-wavenumber data is available, the proof does not resort to the commonly used unphysical CGO solutions. We trace the dependence of the upper bound of the stability estimate on the constant attenuation through an analysis of the resolvent estimates. Both of the stability estimates show exponential dependence on the attenuation coefficient, which illustrates the poor resolution of the inverse scattering with attenuation.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"431 ","pages":"Article 113259"},"PeriodicalIF":2.4,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Chaoticity of generic points for ergodic measures in hyperbolic systems and beyond","authors":"Xiaobo Hou,&nbsp;Xueting Tian,&nbsp;Xutong Zhao","doi":"10.1016/j.jde.2025.113236","DOIUrl":"10.1016/j.jde.2025.113236","url":null,"abstract":"<div><div>In this paper, we search the chaotic behavior in the set of generic points of ergodic measures (called the Birkhoff basin) and find several types of chaoticity stronger than Li-Yorke chaos. More precisely, we consider nonuniformly hyperbolic systems first. On one hand, the Birkhoff basin of every ergodic hyperbolic measure with positive metric entropy exhibits a type of distributional chaos property between DC1 and Li-Yorke chaos, called Banach DC1. On the other hand, the Birkhoff basin of every totally ergodic hyperbolic measure with nondegenerate support exhibits a type of distributional chaos property between DC1 and DC2, called almost DC1. For hyperbolic systems, the Birkhoff basin of every ergodic measure with nondegenerate support from an elementary part of an Axiom A system exhibits both almost DC1 and Banach DC1, and the Birkhoff basin of any trivial ergodic measure supported on some fixed point exhibits Banach DC1 but no almost DC1.</div><div>In this process, Katok's shadowing and horseshoe approximation motivate us to obtain two types of weak specification property as useful techniques to reach our results. Such weak specifications are also valid to symbolic systems like sofic subshifts and <em>β</em>-shifts, so we put them as abstract frameworks in the proof part. Compared with Chen-Tian's result <span><span>[1]</span></span> considering the ergodic measures whose Birkhoff basin has a distal pair, we need to overcome general ergodic measures without the assumption of a distal pair and overcome the nonuniform difficulties from the weak specification property.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"436 ","pages":"Article 113236"},"PeriodicalIF":2.4,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143681725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Second order regularity for solutions to anisotropic degenerate elliptic equations","authors":"Daniel Baratta,&nbsp;Luigi Muglia,&nbsp;Domenico Vuono","doi":"10.1016/j.jde.2025.113250","DOIUrl":"10.1016/j.jde.2025.113250","url":null,"abstract":"<div><div>We consider solutions to degenerate anisotropic elliptic equations in order to study their regularity. In particular we establish second-order estimates and enclose regularity results for the stress field. All our results are new even in the euclidean case.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"435 ","pages":"Article 113250"},"PeriodicalIF":2.4,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A 2D stochastic nonlinearly coupled fluid-structure interaction problem in compliant arteries with unrestricted structural displacement","authors":"Krutika Tawri","doi":"10.1016/j.jde.2025.113243","DOIUrl":"10.1016/j.jde.2025.113243","url":null,"abstract":"<div><div>In this paper, we study a nonlinear fluid-structure interaction (FSI) problem driven by a multiplicative, white-in-time noise. The problem consists of the Navier-Stokes equations describing the flow of an incompressible, viscous fluid in a 2D cylinder interacting with an elastic wall whose elastodynamics is described by membrane/shell equations. The stochastic force is applied both to the fluid equations as a volumetric body force, and to the structure as an external forcing to the deformable fluid boundary. The fluid and the structure are nonlinearly coupled via the kinematic and dynamic conditions assumed at the moving interface, which is a random variable not known a priori. Majority of the existing FSI literature builds on the assumption that the structure can only be deformed radially, neglecting its longitudinal displacement. In this article, we consider the case where the structure is allowed to have vectorial (unrestricted) deformations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"431 ","pages":"Article 113243"},"PeriodicalIF":2.4,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Smoothing effects and maximal Hölder regularity for non-autonomous Kolmogorov equations in infinite dimension","authors":"Sandra Cerrai ,&nbsp;Alessandra Lunardi","doi":"10.1016/j.jde.2025.113245","DOIUrl":"10.1016/j.jde.2025.113245","url":null,"abstract":"<div><div>We prove smoothing properties and optimal Schauder type estimates for a class of nonautonomous evolution equations driven by time dependent Ornstein-Uhlenbeck operators in a separable Hilbert space. They arise as Kolmogorov equations of linear nonautonomous stochastic differential equations with Gaussian noise.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"434 ","pages":"Article 113245"},"PeriodicalIF":2.4,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143684983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}