Journal of Differential Equations最新文献

{"title":"On the borderline regularity criterion in anisotropic Lebesgue spaces of the Navier-Stokes equations","authors":"Yanqing Wang ,&nbsp;Wei Wei ,&nbsp;Gang Wu ,&nbsp;Daoguo Zhou","doi":"10.1016/j.jde.2025.113351","DOIUrl":"10.1016/j.jde.2025.113351","url":null,"abstract":"<div><div>In this paper, we are concerned with the critical mixed norm regularity of Leray-Hopf weak solutions of the Navier-Stokes equations in three dimensions and higher dimensions. It is shown that <span><math><mi>u</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>;</mo><msup><mrow><mi>L</mi></mrow><mrow><mover><mrow><mi>q</mi></mrow><mrow><mo>→</mo></mrow></mover></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo><mo>)</mo></math></span> with <span><math><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></munderover><mfrac><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi>q</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfrac><mo>=</mo><mn>1</mn></math></span> ensure that Leray-Hopf weak solutions are regular. A new ingredient is <em>ε</em>-regularity criterion derived by the De Giorgi iteration technique under this critical regularity in high spatial dimension.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"438 ","pages":"Article 113351"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870203","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":"Expansion coefficients and their relation for Melnikov functions near polycycles","authors":"Feng Liang ,&nbsp;Maoan Han","doi":"10.1016/j.jde.2025.113312","DOIUrl":"10.1016/j.jde.2025.113312","url":null,"abstract":"<div><div>Under a suitable assumption we obtain some new results on expansion coefficients and their relation for the first order Melnikov functions near any <em>m</em>-polycycle with hyperbolic saddles, <span><math><mi>m</mi><mo>∈</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>, which establish a general bifurcation theory on limit cycles near the <em>m</em>-polycycles. As an application we consider 2-polycyclic bifurcations for a <em>φ</em>-Laplacian Liénard system and gain the number of limit cycles near the polycycle with two hyperbolic saddles.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"435 ","pages":"Article 113312"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869155","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 determination of the bifurcation type for a free boundary problem modeling tumor growth","authors":"Xinyue Evelyn Zhao ,&nbsp;Junping Shi","doi":"10.1016/j.jde.2025.113352","DOIUrl":"10.1016/j.jde.2025.113352","url":null,"abstract":"<div><div>Many mathematical models in different disciplines involve the formulation of free boundary problems, where the domain boundaries are not predefined. These models present unique challenges, notably the nonlinear coupling between the solution and the boundary, which complicates the identification of bifurcation types. This paper mainly investigates the structure of symmetry-breaking bifurcations in a two-dimensional free boundary problem modeling tumor growth. By expanding the solution to a high order with respect to a small parameter and computing the bifurcation direction at each bifurcation point, we demonstrate that all the symmetry-breaking bifurcations occurred in the model, as established by the Crandall-Rabinowitz Bifurcation From Simple Eigenvalue Theorem, are pitchfork bifurcations. These findings reveal distinct behaviors between the two-dimensional and three-dimensional cases of the same model.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"436 ","pages":"Article 113352"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868175","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":"Asymptotics for quasilinear wave equations in exterior domains","authors":"Weimin Peng ,&nbsp;Dongbing Zha","doi":"10.1016/j.jde.2025.113353","DOIUrl":"10.1016/j.jde.2025.113353","url":null,"abstract":"<div><div>The main concern of this paper is the asymptotic behavior of global classical solution to exterior domain problem for three-dimensional quasilinear wave equations satisfying null condition, in the small data setting. For this purpose, we first provide an alternative proof for the global existence result via purely energy approach, in which only the general derivatives and spatial rotation operators are employed as commuting vector fields. Then based on this new proof, we show that the global solution will scatter, that is, it will converge to some solution of homogeneous linear wave equations, in the energy sense, as time tends to infinity. We also show that the global solution can be determined by the scattering data uniquely, i.e., the inverse scattering property holds.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"437 ","pages":"Article 113353"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869742","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":"Stochastic porous media equation with Robin boundary conditions, gravity-driven infiltration and multiplicative noise","authors":"Ioana Ciotir ,&nbsp;Dan Goreac ,&nbsp;Juan Li ,&nbsp;Antoine Tonnoir","doi":"10.1016/j.jde.2025.113363","DOIUrl":"10.1016/j.jde.2025.113363","url":null,"abstract":"<div><div>We aim at studying a novel mathematical model associated to a physical phenomenon of infiltration in an homogeneous porous medium. The particularities of our system are connected to the presence of a gravitational acceleration term proportional to the level of saturation, and of a Brownian multiplicative perturbation. Furthermore, the boundary conditions intervene in a Robin manner with the distinction of the behavior along the inflow and outflow respectively. We provide qualitative results of well-posedness, the investigation being conducted through a functional approach.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"438 ","pages":"Article 113363"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870204","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":"Reverse Faber-Krahn and Szegő-Weinberger type inequalities for annular domains under Robin-Neumann boundary conditions","authors":"T.V. Anoop ,&nbsp;Vladimir Bobkov ,&nbsp;Pavel Drábek","doi":"10.1016/j.jde.2025.113354","DOIUrl":"10.1016/j.jde.2025.113354","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Let &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&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; be the &lt;em&gt;k&lt;/em&gt;-th eigenvalue of the Laplace operator in a bounded domain Ω of the form &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mtext&gt;out&lt;/mtext&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∖&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mo&gt;‾&lt;/mo&gt;&lt;/mover&gt;&lt;/math&gt;&lt;/span&gt; under the Neumann boundary condition on &lt;span&gt;&lt;math&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mtext&gt;out&lt;/mtext&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and the Robin boundary condition with parameter &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&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;mo&gt;,&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; on the sphere &lt;span&gt;&lt;math&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; of radius &lt;span&gt;&lt;math&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; centered at the origin, the limiting case &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; being understood as the Dirichlet boundary condition on &lt;span&gt;&lt;math&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. In the case &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, it is known that the first eigenvalue &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&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; does not exceed &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∖&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&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;, where &lt;span&gt;&lt;math&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; is chosen such that &lt;span&gt;&lt;math&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∖&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&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;, which can be regarded as a reverse Faber-Krahn type inequality. We establish this result for any &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&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;mo&gt;,&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. Moreover, we provide related estimates for higher eigenvalues under additional geometric assumptions on Ω, which can be seen as Szegő-Weinberger type inequalities. A few counterexamples to the obtained inequalities for domains violating imposed geometric assumptions are given. As auxiliary information, we investigate shapes of eigenfunctions associated with several eigenvalues &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∖&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&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; and show that they are nonradial at least for all positive and all sufficiently negative &lt;em&gt;h&lt;/em&gt; when ","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"437 ","pages":"Article 113354"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869743","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":"Asymptotic behavior of solutions to the Cauchy problem for 1D p-system with spatiotemporal damping: Case 1. v+ = v−","authors":"Yang Cai ,&nbsp;Changchun Liu ,&nbsp;Ming Mei ,&nbsp;Zejia Wang","doi":"10.1016/j.jde.2025.113347","DOIUrl":"10.1016/j.jde.2025.113347","url":null,"abstract":"<div><div>This paper investigates the Cauchy problem for the <em>p</em>-system with spatiotemporal damping, modeling one-dimensional compressible flow through porous media in Lagrangian coordinates. We focus on the large-time asymptotic behavior of the system's solutions when the state constants for the specific volume are the same: <span><math><msub><mrow><mi>v</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>=</mo><msub><mrow><mi>v</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span>, but the state constants for the velocity are different: <span><math><msub><mrow><mi>u</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>≠</mo><msub><mrow><mi>u</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span>. We show the convergence of the solutions to their diffusion waves with the different algebraic time decay rates according to different exponent of time-damping: <span><math><mn>0</mn><mo>≤</mo><mi>λ</mi><mo>&lt;</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>5</mn></mrow></mfrac></math></span>, <span><math><mi>λ</mi><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>5</mn></mrow></mfrac></math></span> and <span><math><mfrac><mrow><mn>3</mn></mrow><mrow><mn>5</mn></mrow></mfrac><mo>&lt;</mo><mi>λ</mi><mo>&lt;</mo><mn>1</mn></math></span>, respectively. Our analysis employs an energy method to establish a series of a priori estimates, offering new insights and theoretical support for understanding the long-time dynamics of compressible flows in porous media with spatially heterogeneous damping.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"436 ","pages":"Article 113347"},"PeriodicalIF":2.4,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143865114","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":"Positive nonradial solutions of an elliptic equation with critical advection term","authors":"A. Aghajani ,&nbsp;C. Cowan","doi":"10.1016/j.jde.2025.113346","DOIUrl":"10.1016/j.jde.2025.113346","url":null,"abstract":"<div><div>Consider the problem<span><span><span>(1)</span><span><math><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>−</mo><mfrac><mrow><mi>β</mi><mi>x</mi><mo>⋅</mo><mi>∇</mi><mi>u</mi></mrow><mrow><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>+</mo><mi>u</mi><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msup><mtext> in </mtext><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo></math></span></span></span> where <span><math><mi>p</mi><mo>&gt;</mo><mn>2</mn></math></span>, <span><math><mi>β</mi><mo>&gt;</mo><mn>0</mn></math></span> and <span><math><mi>N</mi><mo>=</mo><mn>2</mn><mi>n</mi><mo>≥</mo><mn>4</mn></math></span> an even integer. In this work we are interested in finding positive classical nonradial solutions of <span><span>(1)</span></span>. We also consider the problem on the unit ball. We demonstrate the existence of a positive bounded solution for the range <span><math><mn>2</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>:</mo><mo>=</mo><mfrac><mrow><mi>N</mi><mo>+</mo><mn>2</mn><mi>β</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>2</mn><mo>+</mo><mi>β</mi></mrow></mfrac></math></span>, and show that nonradial solutions exist for a specific range of <em>p</em>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"436 ","pages":"Article 113346"},"PeriodicalIF":2.4,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143865115","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 hyperbolic relaxation approximation of the incompressible Navier-Stokes equations with artificial compressibility","authors":"Qian Huang ,&nbsp;Christian Rohde ,&nbsp;Wen-An Yong ,&nbsp;Ruixi Zhang","doi":"10.1016/j.jde.2025.113339","DOIUrl":"10.1016/j.jde.2025.113339","url":null,"abstract":"<div><div>We introduce a new hyperbolic approximation to the incompressible Navier-Stokes equations by incorporating a first-order relaxation and using the artificial compressibility method. With two relaxation parameters in the model, we rigorously prove the asymptotic limit of the system towards the incompressible Navier-Stokes equations as both parameters tend to zero. Notably, the convergence of the approximate pressure variable is achieved by the help of a linear ‘auxiliary’ system and energy-type error estimates of the differences between the two-parameter model and the Navier-Stokes equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"438 ","pages":"Article 113339"},"PeriodicalIF":2.4,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870202","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 Calderón-Zygmund theory for fractional Laplacian type equations","authors":"Sun-Sig Byun ,&nbsp;Kyeongbae Kim ,&nbsp;Deepak Kumar","doi":"10.1016/j.jde.2025.113319","DOIUrl":"10.1016/j.jde.2025.113319","url":null,"abstract":"<div><div>We establish several fine boundary regularity results of weak solutions to non-homogeneous <em>s</em>-fractional Laplacian type equations. In particular, we prove sharp Calderón-Zygmund type estimates of <span><math><mi>u</mi><mo>/</mo><msup><mrow><mi>d</mi></mrow><mrow><mi>s</mi></mrow></msup></math></span> depending on the regularity assumptions on the associated kernel coefficient including VMO, Dini continuity or the Hölder continuity, where <em>u</em> is a weak solution to such a nonlocal problem and <em>d</em> is the distance to the boundary function of a given domain. Our analysis is based on point-wise behaviors of maximal functions of <span><math><mi>u</mi><mo>/</mo><msup><mrow><mi>d</mi></mrow><mrow><mi>s</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"436 ","pages":"Article 113319"},"PeriodicalIF":2.4,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143860718","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}