Journal of Differential Equations最新文献

{"title":"On the stationary magneto-convective motion of compressible full MHD equations in an infinite horizontal layer","authors":"Rachid Benabidallah ,&nbsp;François Ebobisse ,&nbsp;Mohamed Azouz","doi":"10.1016/j.jde.2025.113744","DOIUrl":"10.1016/j.jde.2025.113744","url":null,"abstract":"<div><div>In an infinite horizontal layer, we consider the equations of the viscous, compressible, and heat conducting magnetohydrodynamic steady flows subject to the gravitational force and to a large gradient of the temperature across the layer. As boundary conditions, we assume in the vertical directions, slip-boundary for the velocity and vertical conditions for magnetic field. The existence of a stationary solution in a small neighborhood of a steady profile close to the rest state is obtained in the Sobolev spaces as limit of a sequence of fixed points of some operators constructed from a suitable linearization of the full magnetohydrodynamic system of equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113744"},"PeriodicalIF":2.3,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046534","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 the critical behavior for the semilinear biharmonic heat equation with forcing term in exterior domain","authors":"Nurdaulet N. Tobakhanov ,&nbsp;Berikbol T. Torebek","doi":"10.1016/j.jde.2025.113758","DOIUrl":"10.1016/j.jde.2025.113758","url":null,"abstract":"<div><div>In this paper, we investigate the critical behavior of solutions to the semilinear biharmonic heat equation with forcing term <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span>, under six homogeneous boundary conditions. This paper is the first since the seminal work by Bandle et al. (2000) <span><span>[24]</span></span>, to focus on the study of critical exponents in exterior problems for semilinear parabolic equations with a forcing term. By employing a method of test functions and comparison principle, we derive the critical exponents <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>C</mi><mi>r</mi><mi>i</mi><mi>t</mi></mrow></msub></math></span> in the sense of Fujita. Moreover, we show that <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>C</mi><mi>r</mi><mi>i</mi><mi>t</mi></mrow></msub><mo>=</mo><mo>∞</mo></math></span> if <span><math><mi>N</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn></math></span> and <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>C</mi><mi>r</mi><mi>i</mi><mi>t</mi></mrow></msub><mo>=</mo><mfrac><mrow><mi>N</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>4</mn></mrow></mfrac></math></span> if <span><math><mi>N</mi><mo>⩾</mo><mn>5</mn></math></span>. The impact of the forcing term on the critical behavior of the problem is also of interest, and thus a second critical exponent in the sense of Lee-Ni, depending on the forcing term is introduced. We also discuss the case <span><math><mi>f</mi><mo>≡</mo><mn>0</mn></math></span>, and present the finite-time blow-up results and lifespan estimates of solutions for the subcritical and critical cases. The lifespan estimates of solutions are obtained by employing the method proposed by Ikeda and Sobajama (2019) <span><span>[13]</span></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113758"},"PeriodicalIF":2.3,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046532","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 existence results for coupled parabolic systems with general sources and some extensions involving degenerate coefficients","authors":"Brandon Carhuas-Torre ,&nbsp;Ricardo Castillo ,&nbsp;Kerven Cea ,&nbsp;Ricardo Freire ,&nbsp;Alex Lira ,&nbsp;Miguel Loayza","doi":"10.1016/j.jde.2025.113765","DOIUrl":"10.1016/j.jde.2025.113765","url":null,"abstract":"<div><div>This work presents optimal conditions for the existence of global solutions for the coupled parabolic system: <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>=</mo><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo><mi>f</mi><mo>(</mo><mi>v</mi><mo>)</mo></math></span> and <span><math><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><mi>Δ</mi><mi>v</mi><mo>=</mo><mi>l</mi><mo>(</mo><mi>t</mi><mo>)</mo><mi>g</mi><mo>(</mo><mi>u</mi><mo>)</mo></math></span> in <span><math><mi>Ω</mi><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>)</mo></math></span> with the Dirichlet boundary conditions. Here, <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> is a bounded or unbounded domain, the initial data belong to <span><math><msup><mrow><mo>[</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>Ω</mi><mo>)</mo><mo>]</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span>, and the functions <span><math><mi>f</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>l</mi><mo>∈</mo><mi>C</mi><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span>. We also study the coupled parabolic system with degenerate coefficients: <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><mi>div</mi><mo>(</mo><mi>ω</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>∇</mi><mi>u</mi><mo>)</mo><mo>=</mo><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo><mi>f</mi><mo>(</mo><mi>v</mi><mo>)</mo></math></span> and <span><math><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><mi>div</mi><mo>(</mo><mi>ω</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>∇</mi><mi>v</mi><mo>)</mo><mo>=</mo><mi>l</mi><mo>(</mo><mi>t</mi><mo>)</mo><mi>g</mi><mo>(</mo><mi>u</mi><mo>)</mo></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>)</mo></math></span>, where <em>ω</em> belong to the class <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> of Muckenhoupt functions and may exhibit singularities along the line <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn></math></span>. This problem is related to the fractional Laplacian through the Caffarelli-Silvestre extension given in <span><span>[2]</span></span>. In addition, critical Fujita-type exponents are derived for both systems.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113765"},"PeriodicalIF":2.3,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046530","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":"The boundedness of almost-periodic oscillators with asymmetric potentials via normal form theorem","authors":"Shuyi Wang,&nbsp;Min Li,&nbsp;Daxiong Piao","doi":"10.1016/j.jde.2025.113763","DOIUrl":"10.1016/j.jde.2025.113763","url":null,"abstract":"<div><div>This paper investigates the boundedness of solutions for the semilinear asymmetric oscillator<span><span><span><math><mrow><mover><mrow><mi>x</mi></mrow><mrow><mo>¨</mo></mrow></mover><mo>+</mo><mi>a</mi><msup><mrow><mi>x</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>−</mo><mi>b</mi><msup><mrow><mi>x</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>=</mo><mi>p</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>,</mo></mrow></math></span></span></span> where <em>p</em> is real analytic and almost-periodic function with infinitely many rationally independent frequencies. A key contribution is the development of a novel normal form theorem for planar almost-periodic mappings under a weighted Diophantine-type nonresonance condition <span><span>(1.7)</span></span>. Unlike prior approaches relying on twist conditions or spatial averaging, our framework eliminates geometric constraints by leveraging the spatial structure of infinite-dimensional frequencies. As a direct consequence, we prove two main results: 1. The existence of infinitely many almost-periodic solutions; 2. The boundedness of all solutions for the asymmetric oscillator, even when traditional twist integrals (e.g., <span><span>(1.5)</span></span>) vanish. This work unifies periodic/quasi-periodic boundedness theories and extends them to the almost-periodic regime, resolving long-standing limitations in planar Hamiltonian systems with asymmetric potentials.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113763"},"PeriodicalIF":2.3,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145027285","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":"Bifurcation of gravity-capillary Stokes waves with constant vorticity","authors":"T. Barbieri ,&nbsp;M. Berti ,&nbsp;A. Maspero ,&nbsp;M. Mazzucchelli","doi":"10.1016/j.jde.2025.113753","DOIUrl":"10.1016/j.jde.2025.113753","url":null,"abstract":"<div><div>We consider the gravity-capillary water waves equations of a 2D fluid with constant vorticity. By employing variational methods we prove the bifurcation of periodic traveling water waves –which are steady in a moving frame– for <em>all</em> the values of gravity, surface tension, constant vorticity, depth and wavelenght, extending previous results valid for restricted values of the parameters. We parametrize the bifurcating Stokes waves either with their speed or their momentum.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113753"},"PeriodicalIF":2.3,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020204","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":"H2-regularity for stationary and non-stationary Bingham problems with perfect slip boundary condition","authors":"Takeshi Fukao ,&nbsp;Takahito Kashiwabara","doi":"10.1016/j.jde.2025.113739","DOIUrl":"10.1016/j.jde.2025.113739","url":null,"abstract":"<div><div><span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-spatial regularity of stationary and non-stationary problems for Bingham fluids formulated with the pseudo-stress tensor is discussed. The problem is mathematically described by an elliptic or parabolic variational inequality of the second kind, to which weak solvability in the Sobolev space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> is well known. However, higher regularity up to the boundary in a bounded smooth domain seems to remain open. This paper indeed shows such <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-regularity if the problems are supplemented with the so-called perfect slip boundary condition and if the yield stress vanishes on the boundary. For the stationary Bingham–Stokes problem, the key of the proof lies in a priori estimates for a regularized problem avoiding investigation of higher pressure regularity, which seems difficult to get in the presence of a singular diffusion term. The <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-regularity for the stationary case is then directly applied to establish strong solvability of the non-stationary Bingham–Navier–Stokes problem, based on discretization in time and on the truncation of the nonlinear convection term.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113739"},"PeriodicalIF":2.3,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020197","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":"ABP estimate on metric measure spaces via optimal transport","authors":"Bang-Xian Han","doi":"10.1016/j.jde.2025.113757","DOIUrl":"10.1016/j.jde.2025.113757","url":null,"abstract":"<div><div>By using optimal transport theory, we establish a sharp Alexandroff–Bakelman–Pucci (ABP) type estimate on metric measure spaces with synthetic Riemannian Ricci curvature lower bounds, and prove some geometric and functional inequalities including a functional ABP estimate. Our result not only extends the border of ABP estimate, but also provides an effective substitution of Jacobi fields computation in the non-smooth framework, which has potential applications to many problems in non-smooth geometric analysis.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113757"},"PeriodicalIF":2.3,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020199","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":"Reconstruction of Schrödinger operators by half of the Dirichlet eigenvalues","authors":"Xinya Yang ,&nbsp;Guangsheng Wei","doi":"10.1016/j.jde.2025.113747","DOIUrl":"10.1016/j.jde.2025.113747","url":null,"abstract":"<div><div>We present a method for reconstructing the potential of a one-dimensional Schrödinger operator in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> using half of the Dirichlet-Dirichlet spectrum, combined with the potential known a priori on <span><math><mo>[</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>,</mo><mn>1</mn><mo>]</mo></math></span>. This problem relates to the uniqueness theorem due to Gesztesy and Simon <span><span>[2]</span></span> concerning inverse eigenvalue problems with mixed given data. The basic idea is to establish an appropriate functional equation, which enables us to propose a method for recovering the potential in this type of inverse problem. Additionally, we provide a necessary and sufficient condition for the existence of a solution to this problem.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113747"},"PeriodicalIF":2.3,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020203","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 strong solutions of the 3D compressible viscoelastic equations without structure assumptions","authors":"Yifeng Huang,&nbsp;Qingqing Liu,&nbsp;Changjiang Zhu","doi":"10.1016/j.jde.2025.113767","DOIUrl":"10.1016/j.jde.2025.113767","url":null,"abstract":"<div><div>In this paper, we develop Zhu Yi's method (Y. Zhu (2022) <span><span>[29]</span></span>) to prove the global strong solutions of the 3D compressible viscoelastic equations without any additional structure assumptions on the deformation tensor. To obtain the uniform bounds of the density and deformation tensor, the spectral method is used.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"450 ","pages":"Article 113767"},"PeriodicalIF":2.3,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019357","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 of rarefaction wave for steady supersonic relativistic Euler flows past Lipschitz wedges","authors":"Min Ding ,&nbsp;Yachun Li","doi":"10.1016/j.jde.2025.113752","DOIUrl":"10.1016/j.jde.2025.113752","url":null,"abstract":"<div><div>This paper is devoted to studying two-dimensional steady supersonic relativistic Euler flows past a sharp corner or a bending wedge. When the vertex angle is larger than <em>π</em> and the wedge is a small perturbation of a convex rigid wall, we prove the global existence and stability of entropy solution including a large rarefaction wave under some small perturbations of the initial data and the slope of the boundary. Moreover, we obtain global non-relativistic limits of entropy solution as well as the asymptotic behavior of the solution as <span><math><mi>x</mi><mo>→</mo><mo>+</mo><mo>∞</mo></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113752"},"PeriodicalIF":2.3,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020201","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}