Journal of Differential Equations最新文献_第5页

H2-regularity for stationary and non-stationary Bingham problems with perfect slip boundary condition 具有完全滑移边界条件的平稳和非平稳Bingham问题的h2 -正则性

IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-09-08 DOI: 10.1016/j.jde.2025.113739

Takeshi Fukao , Takahito Kashiwabara

{"title":"H2-regularity for stationary and non-stationary Bingham problems with perfect slip boundary condition","authors":"Takeshi Fukao , 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}

引用次数: 0

ABP estimate on metric measure spaces via optimal transport 基于最优运输的度量空间ABP估计

IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-09-08 DOI: 10.1016/j.jde.2025.113757

Bang-Xian Han

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Reconstruction of Schrödinger operators by half of the Dirichlet eigenvalues 用Dirichlet特征值的一半重构Schrödinger算子

IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-09-08 DOI: 10.1016/j.jde.2025.113747

Xinya Yang , Guangsheng Wei

引用次数: 0

Global strong solutions of the 3D compressible viscoelastic equations without structure assumptions 无结构假设的三维可压缩粘弹性方程的全局强解

IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-09-08 DOI: 10.1016/j.jde.2025.113767

Yifeng Huang, Qingqing Liu, Changjiang Zhu

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Stability of rarefaction wave for steady supersonic relativistic Euler flows past Lipschitz wedges 超声速相对论欧拉流通过利普希茨楔时稀疏波的稳定性

IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-09-08 DOI: 10.1016/j.jde.2025.113752

Min Ding , Yachun Li

引用次数: 0

An explicitly solvable NLS model with discontinuous standing waves 具有不连续驻波的显解NLS模型

IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-09-08 DOI: 10.1016/j.jde.2025.113746

Riccardo Adami , Filippo Boni , Takaaki Nakamura , Alice Ruighi

{"title":"An explicitly solvable NLS model with discontinuous standing waves","authors":"Riccardo Adami , Filippo Boni , Takaaki Nakamura , Alice Ruighi","doi":"10.1016/j.jde.2025.113746","DOIUrl":"10.1016/j.jde.2025.113746","url":null,"abstract":"<div><div>We study the NLS Equation on the line with a point interaction given by the superposition of an attractive delta potential with a dipole interaction, in the cases of <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-subcritical and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-critical nonlinearity.</div><div>For a subcritical nonlinearity we prove the existence and the uniqueness of Ground States at any mass. If the mass exceeds an explicit threshold, then there exists a positive excited state too.</div><div>For the critical nonlinearity we prove that Ground States exist only in a specific interval of masses, while in a different interval excited states exist. We provide the value of the optimal constant in the Gagliardo-Nirenberg estimate and describe in the dipole case the branches of the stationary states as the strength of the interaction varies.</div><div>Since all stationary states are explicitly computed, ours is a solvable model involving a non-standard interplay of a nonlinearity with a point interaction.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113746"},"PeriodicalIF":2.3,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020202","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}

引用次数: 0

Morse index and non-degeneracy of double-tower solutions for prescribed scalar curvature problem 给定标量曲率问题双塔解的莫尔斯指数和非简并性

IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-09-08 DOI: 10.1016/j.jde.2025.113751

Yuxia Guo , Yichen Hu , Shaolong Peng

引用次数: 0

Vanishing viscosity limit of compressible non-resistive magnetohydrodynamic equations with the no-slip boundary condition 无滑移边界条件下可压缩无阻力磁流体动力学方程的消失黏度极限

IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-09-05 DOI: 10.1016/j.jde.2025.113749

Qiangchang Ju , Jiawei Wang , Feng Xie

引用次数: 0

Heat equation in a periodic domain with special initial data 具有特殊初始数据的周期域热方程

IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-09-05 DOI: 10.1016/j.jde.2025.113754

Marcus Rosenberg, Jari Taskinen

引用次数: 0

Global-in-time maximal regularity for the Cauchy problem of the heat equation in BMO and applications BMO热方程Cauchy问题的全局时极大正则性及其应用

IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-09-05 DOI: 10.1016/j.jde.2025.113748

Xuan Thinh Duong , Ji Li , Liangchuan Wu , Lixin Yan

{"title":"Global-in-time maximal regularity for the Cauchy problem of the heat equation in BMO and applications","authors":"Xuan Thinh Duong , Ji Li , Liangchuan Wu , Lixin Yan","doi":"10.1016/j.jde.2025.113748","DOIUrl":"10.1016/j.jde.2025.113748","url":null,"abstract":"<div><div>In this article, we establish global-in-time maximal regularity for the Cauchy problem of the classical heat equation <span><math><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></math></span> with <span><math><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>0</mn></math></span> in a certain BMO setting, which improves the local-in-time result initially proposed by Ogawa and Shimizu in <span><span>[26]</span></span>, <span><span>[27]</span></span>. In further developing our method originally formulated for the heat equation, we obtain analogous global BMO-maximal regularity associated to the Schrödinger operator <span><math><mi>L</mi><mo>=</mo><mo>−</mo><mi>Δ</mi><mo>+</mo><mi>V</mi></math></span>, where the nonnegative potential <em>V</em> belongs to the reverse Hölder class <span><math><msub><mrow><mi>RH</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span> for some <span><math><mi>q</mi><mo>></mo><mi>n</mi><mo>/</mo><mn>2</mn></math></span>. This extension includes several inhomogeneous estimates as ingredients, such as Carleson-type estimates for the external forces.</div><div>Our new methodology is to exploit elaborate heat kernel estimates, along with matched space-time decomposition on the involving integral-type structure of maximal operators, as well as some global techniques such as those from de Simon's work and Schur's lemma. One crucial trick is to utilize the mean oscillation therein to contribute a higher and necessary decay order for global-in-time estimates.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113748"},"PeriodicalIF":2.3,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144997555","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}

引用次数: 0