Pub Date : 2026-05-05Epub Date: 2026-02-26DOI: 10.1016/j.jde.2026.114242
Bauyrzhan Derbissaly
We study the Steklov eigenvalue problem for a linear, isotropic micropolar (Cosserat) elastic solid, where the spectral parameter enters boundary conditions that link tangential tractions to tangential boundary fields. We formulate the problem in strong and weak forms, identify the Dirichlet-to-Neumann map on the boundary, and prove discreteness of the spectrum. Using a microlocal analysis of this map, we establish a Weyl law with an explicit coefficient expressed in terms of the Cosserat moduli. We also analyze spectral stability under high-frequency boundary perturbations.
{"title":"The Steklov eigenproblem for a micropolar elastic solid","authors":"Bauyrzhan Derbissaly","doi":"10.1016/j.jde.2026.114242","DOIUrl":"10.1016/j.jde.2026.114242","url":null,"abstract":"<div><div>We study the Steklov eigenvalue problem for a linear, isotropic micropolar (Cosserat) elastic solid, where the spectral parameter enters boundary conditions that link tangential tractions to tangential boundary fields. We formulate the problem in strong and weak forms, identify the Dirichlet-to-Neumann map on the boundary, and prove discreteness of the spectrum. Using a microlocal analysis of this map, we establish a Weyl law with an explicit coefficient expressed in terms of the Cosserat moduli. We also analyze spectral stability under high-frequency boundary perturbations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"462 ","pages":"Article 114242"},"PeriodicalIF":2.3,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385050","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}
Pub Date : 2026-05-05Epub Date: 2026-01-26DOI: 10.1016/j.jde.2026.114155
Yingdu Dong, Xiong Li
In this paper, we focus on the existence of rotating wave solutions for a nonlinear wave equation on the sphere with , which is a kind of traveling wave solutions on non-Euclidean spaces. The case when the angular velocity is larger than 1 is of particular focus, as it leads to an elliptic-hyperbolic mixed-type equation. Generally, the spectrum of a mixed-type linearized operator could behave badly, e.g., the spectrum is unbounded from below and above, and there may exist an accumulation at zero. The aim of this paper is to address the case with accumulation points in the spectrum, which leads to the ‘small divisor problem’. Owing to the geometric structure of the sphere and the good properties of the eigenvalues of the Laplacian on it, the accumulation can occur in a controlled manner if appropriate angular velocities are selected. Then we attack this issue through the Nash-Moser type iteration theorem.
{"title":"Rotating waves for nonlinear wave equations with angular velocities on a positive-measure set","authors":"Yingdu Dong, Xiong Li","doi":"10.1016/j.jde.2026.114155","DOIUrl":"10.1016/j.jde.2026.114155","url":null,"abstract":"<div><div>In this paper, we focus on the existence of rotating wave solutions for a nonlinear wave equation on the sphere <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span> with <span><math><mi>d</mi><mo>≥</mo><mn>3</mn></math></span>, which is a kind of traveling wave solutions on non-Euclidean spaces. The case when the angular velocity is larger than 1 is of particular focus, as it leads to an elliptic-hyperbolic mixed-type equation. Generally, the spectrum of a mixed-type linearized operator could behave badly, e.g., the spectrum is unbounded from below and above, and there may exist an accumulation at zero. The aim of this paper is to address the case with accumulation points in the spectrum, which leads to the ‘small divisor problem’. Owing to the geometric structure of the sphere and the good properties of the eigenvalues of the Laplacian on it, the accumulation can occur in a controlled manner if appropriate angular velocities are selected. Then we attack this issue through the Nash-Moser type iteration theorem.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"462 ","pages":"Article 114155"},"PeriodicalIF":2.3,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146075450","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}
Pub Date : 2026-05-05Epub Date: 2026-02-04DOI: 10.1016/j.jde.2026.114166
Fei Wang , Zeren Zhang
We address a threshold problem of the Couette flow in a uniform magnetic field for the 2D MHD equation on with fluid viscosity ν and magnetic resistivity μ. The nonlinear enhanced dissipation and inviscid damping are also established. In particularly, when , we get a threshold in . When , we obtain a threshold , hence improving the results in [19], [14], [22].
{"title":"The stability threshold for 2D MHD equations around Couette with general viscosity and magnetic resistivity","authors":"Fei Wang , Zeren Zhang","doi":"10.1016/j.jde.2026.114166","DOIUrl":"10.1016/j.jde.2026.114166","url":null,"abstract":"<div><div>We address a threshold problem of the Couette flow <span><math><mo>(</mo><mi>y</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></span> in a uniform magnetic field <span><math><mo>(</mo><mi>β</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></span> for the 2D MHD equation on <span><math><mi>T</mi><mo>×</mo><mi>R</mi></math></span> with fluid viscosity <em>ν</em> and magnetic resistivity <em>μ</em>. The nonlinear enhanced dissipation and inviscid damping are also established. In particularly, when <span><math><mn>0</mn><mo><</mo><mi>ν</mi><mo>≤</mo><msup><mrow><mi>μ</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>≤</mo><mn>1</mn></math></span>, we get a threshold <span><math><msup><mrow><mi>ν</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></msup></math></span> in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>(</mo><mi>N</mi><mo>≥</mo><mn>4</mn><mo>)</mo></math></span>. When <span><math><mn>0</mn><mo><</mo><msup><mrow><mi>μ</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>≤</mo><mi>ν</mi><mo>≤</mo><mn>1</mn></math></span>, we obtain a threshold <span><math><mi>min</mi><mo></mo><mo>{</mo><msup><mrow><mi>ν</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo>,</mo><msup><mrow><mi>μ</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo>}</mo><mi>min</mi><mo></mo><mo>{</mo><mn>1</mn><mo>,</mo><msup><mrow><mi>ν</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></msup><mo>}</mo></math></span>, hence improving the results in <span><span>[19]</span></span>, <span><span>[14]</span></span>, <span><span>[22]</span></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"462 ","pages":"Article 114166"},"PeriodicalIF":2.3,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146170548","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}
Pub Date : 2026-05-05Epub Date: 2026-01-23DOI: 10.1016/j.jde.2026.114137
Shengchuang Chang , Shuangqian Liu , Tong Yang
The spatially homogeneous Vlasov-Nordström-Fokker-Planck system is known to exhibit nontrivial large time behavior, naturally leading to weak diffusion of the Fokker-Planck operator. This weak diffusion, combined with the singularity of relativistic velocity, presents a significant challenge in analysis for the spatially inhomogeneous counterpart.
In this paper, we demonstrate that the Cauchy problem for the spatially inhomogeneous Vlasov-Nordström-Fokker-Planck system, without friction, maintains dynamically stable relative to the corresponding spatially homogeneous system. Our results are twofold: (1) we establish the existence of a unique global classical solution and characterize the asymptotic behavior of the spatially inhomogeneous system using a refined weighted energy method; (2) we directly verify the dynamic stability of the spatially inhomogeneous system in the framework of rescaled solutions.
{"title":"The spatially inhomogeneous Vlasov-Nordström-Fokker-Planck system in the intrinsic weak diffusion regime","authors":"Shengchuang Chang , Shuangqian Liu , Tong Yang","doi":"10.1016/j.jde.2026.114137","DOIUrl":"10.1016/j.jde.2026.114137","url":null,"abstract":"<div><div>The spatially homogeneous Vlasov-Nordström-Fokker-Planck system is known to exhibit nontrivial large time behavior, naturally leading to weak diffusion of the Fokker-Planck operator. This weak diffusion, combined with the singularity of relativistic velocity, presents a significant challenge in analysis for the spatially inhomogeneous counterpart.</div><div>In this paper, we demonstrate that the Cauchy problem for the spatially inhomogeneous Vlasov-Nordström-Fokker-Planck system, without friction, maintains dynamically stable relative to the corresponding spatially homogeneous system. Our results are twofold: (1) we establish the existence of a unique global classical solution and characterize the asymptotic behavior of the spatially inhomogeneous system using a refined weighted energy method; (2) we directly verify the dynamic stability of the spatially inhomogeneous system in the framework of rescaled solutions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"462 ","pages":"Article 114137"},"PeriodicalIF":2.3,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025658","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}
Pub Date : 2026-05-05Epub Date: 2026-02-17DOI: 10.1016/j.jde.2026.114235
Simone Ciani , Eurica Henriques , Mariia O. Savchenko , Igor I. Skrypnik
We define a suitable class of functions bearing unbalanced energy estimates, that are embodied by local weak subsolutions to doubly nonlinear, double-phase, Orlicz-type and fully anisotropic operators. Then we prove that members of are locally bounded, under critical, sub-critical and limit growth conditions typical of singular and degenerate parabolic operators, with quantitative point-wise estimates that follow the lines of the pioneering work of Ladyzhenskaya, Solonnikov and Uraltseva [31]. These local bounds are new in the critical case and sub-critical cases, and have been obtained without any qualitative boundedness assumption. In particular, our proof of local boundedness in the critical case is valid disregarding of any additional integrability conditions and covers both the classical p-Laplacian and the porous medium equations.
{"title":"Parabolic De Giorgi classes with doubly nonlinear, nonstandard growth: local boundedness under exact integrability assumptions","authors":"Simone Ciani , Eurica Henriques , Mariia O. Savchenko , Igor I. Skrypnik","doi":"10.1016/j.jde.2026.114235","DOIUrl":"10.1016/j.jde.2026.114235","url":null,"abstract":"<div><div>We define a suitable class <span><math><mi>PDG</mi></math></span> of functions bearing unbalanced energy estimates, that are embodied by local weak subsolutions to doubly nonlinear, double-phase, Orlicz-type and fully anisotropic operators. Then we prove that members of <span><math><mi>PDG</mi></math></span> are locally bounded, under critical, sub-critical and limit growth conditions typical of singular and degenerate parabolic operators, with quantitative point-wise estimates that follow the lines of the pioneering work of Ladyzhenskaya, Solonnikov and Uraltseva <span><span>[31]</span></span>. These local bounds are new in the critical case and sub-critical cases, and have been obtained without any qualitative boundedness assumption. In particular, our proof of local boundedness in the critical case is valid disregarding of any additional integrability conditions and covers both the classical <em>p</em>-Laplacian and the porous medium equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"462 ","pages":"Article 114235"},"PeriodicalIF":2.3,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385056","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}
Pub Date : 2026-05-05Epub Date: 2026-01-28DOI: 10.1016/j.jde.2026.114144
Xiandong Lin , Hailong Ye , Xiao-Qiang Zhao
We propose a class of nonlocal dispersal systems on time-varying domains, and fully characterize their asymptotic dynamics in the asymptotically fixed, time-periodic and unbounded cases. We first establish the comparison principle for generalized sub- and supersolutions of a class of nonautonomous nonlocal dispersal systems defined on the space of bounded measurable functions. Based on this, we develop a comprehensive framework to rigorously examine the threshold dynamics of the original system on asymptotically fixed and time-periodic domains. In the asymptotically unbounded case, we introduce a key auxiliary function to address the difficulties caused by the vanishing viscosity as , and the time-dependent coupling structure in the nonlocal kernels. This enables us to construct generalized subsolutions and derive the global threshold dynamics via the comparison principle. The findings may be of independent interest and the developed techniques are expected to find further applications in the related nonlocal dispersal problems. We also conduct numerical simulations for a practical model to illustrate our analytical results.
{"title":"Global dynamics of nonlocal dispersal systems on time-varying domains","authors":"Xiandong Lin , Hailong Ye , Xiao-Qiang Zhao","doi":"10.1016/j.jde.2026.114144","DOIUrl":"10.1016/j.jde.2026.114144","url":null,"abstract":"<div><div>We propose a class of nonlocal dispersal systems on time-varying domains, and fully characterize their asymptotic dynamics in the asymptotically fixed, time-periodic and unbounded cases. We first establish the comparison principle for generalized sub- and supersolutions of a class of nonautonomous nonlocal dispersal systems defined on the space of bounded measurable functions. Based on this, we develop a comprehensive framework to rigorously examine the threshold dynamics of the original system on asymptotically fixed and time-periodic domains. In the asymptotically unbounded case, we introduce a key auxiliary function to address the difficulties caused by the vanishing viscosity as <span><math><mi>t</mi><mo>→</mo><mo>∞</mo></math></span>, and the time-dependent coupling structure in the nonlocal kernels. This enables us to construct generalized subsolutions and derive the global threshold dynamics via the comparison principle. The findings may be of independent interest and the developed techniques are expected to find further applications in the related nonlocal dispersal problems. We also conduct numerical simulations for a practical model to illustrate our analytical results.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"462 ","pages":"Article 114144"},"PeriodicalIF":2.3,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146075453","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}
Pub Date : 2026-04-25Epub Date: 2026-01-09DOI: 10.1016/j.jde.2026.114096
Peng Shi , Yan-Xia Feng , Wan-Tong Li , Fei-Ying Yang
Recent studies indicate that in many epidemics, the strains (bacterial or viral) of disease-causing pathogens exhibit significant diversity, and human mobility patterns follow scale-free, nonlocal dynamics characterized by heavy-tailed distributions such as Lévy flights. To investigate the long-range geographical spread of multi-strain epidemics, this article proposes a multi-strain susceptible-infected-susceptible (SIS) model incorporating fractional diffusion. The central questions addressed in our study include the competitive exclusion and coexistence of multiple strains, as well as the influence of fractional powers and dispersal rates on the asymptotic behavior of equilibrium solutions. Our analysis demonstrates that: (i) the basic reproduction number acts as a threshold for disease extinction; (ii) the invasion number serves as a threshold for both the existence and stability of the coexistence equilibrium and the stability of single-strain endemic equilibria. Additionally, we examine the effect of home and hospital isolation measures on disease transmission.
{"title":"Spatiotemporal dynamics in a multi-strain epidemic model with fractional diffusion","authors":"Peng Shi , Yan-Xia Feng , Wan-Tong Li , Fei-Ying Yang","doi":"10.1016/j.jde.2026.114096","DOIUrl":"10.1016/j.jde.2026.114096","url":null,"abstract":"<div><div>Recent studies indicate that in many epidemics, the strains (bacterial or viral) of disease-causing pathogens exhibit significant diversity, and human mobility patterns follow scale-free, nonlocal dynamics characterized by heavy-tailed distributions such as Lévy flights. To investigate the long-range geographical spread of multi-strain epidemics, this article proposes a multi-strain susceptible-infected-susceptible (SIS) model incorporating fractional diffusion. The central questions addressed in our study include the competitive exclusion and coexistence of multiple strains, as well as the influence of fractional powers and dispersal rates on the asymptotic behavior of equilibrium solutions. Our analysis demonstrates that: (i) the basic reproduction number acts as a threshold for disease extinction; (ii) the invasion number serves as a threshold for both the existence and stability of the coexistence equilibrium and the stability of single-strain endemic equilibria. Additionally, we examine the effect of home and hospital isolation measures on disease transmission.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"461 ","pages":"Article 114096"},"PeriodicalIF":2.3,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145924239","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}
Pub Date : 2026-04-25Epub Date: 2026-01-13DOI: 10.1016/j.jde.2026.114094
Yang Cai , Changchun Liu , Ming Mei , Zejia Wang
This paper is concerned with the Cauchy problem for 1D compressible Euler equations with spatiotemporal damping in the critical case. We prove the existence of the solutions and their new convergence to the special diffusion waves by the technical time-weighted energy method, where the convergence rates are dependent on the spatial state of the spatiotemporal damping as . These convergence results significantly improve and develop the previous studies of Geng et al. (2020) [10] and Matsumura and Nishihara (2024) [24].
研究具有时空阻尼的一维可压缩欧拉方程在临界情况下的Cauchy问题。我们用技术时间加权能量法证明了该类扩散波解的存在性及其新的收敛性，其中收敛速率依赖于时空阻尼的空间状态为x→±∞。这些收敛结果显著改进和发展了Geng et al.(2020)[10]和Matsumura and Nishihara(2024)[24]的先前研究。
{"title":"Novel convergence of solutions to 1D compressible Euler equations with spatiotemporal damping in critical case","authors":"Yang Cai , Changchun Liu , Ming Mei , Zejia Wang","doi":"10.1016/j.jde.2026.114094","DOIUrl":"10.1016/j.jde.2026.114094","url":null,"abstract":"<div><div>This paper is concerned with the Cauchy problem for 1D compressible Euler equations with spatiotemporal damping in the critical case. We prove the existence of the solutions and their new convergence to the special diffusion waves by the technical time-weighted energy method, where the convergence rates are dependent on the spatial state of the spatiotemporal damping as <span><math><mi>x</mi><mo>→</mo><mo>±</mo><mo>∞</mo></math></span>. These convergence results significantly improve and develop the previous studies of Geng et al. (2020) <span><span>[10]</span></span> and Matsumura and Nishihara (2024) <span><span>[24]</span></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"461 ","pages":"Article 114094"},"PeriodicalIF":2.3,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980539","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}
Pub Date : 2026-04-25Epub Date: 2026-01-16DOI: 10.1016/j.jde.2026.114114
Chun Liu , Suliang Si , Guanghui Hu , Bo Zhang
This paper is concerned with the inverse source problems for the acoustic wave equation in the full space , where the source term is compactly supported in both time and spatial variables. The main goal is to investigate increasing stability for the wave equation in terms of the interval length of given parameters (e.g., frequency bandwith of the temporal component of the source function). We establish increasing stability estimates of the -norm of the source function by using only the Dirichlet boundary data. Our method relies on the Huygens' principle, the Fourier transform and explicit bounds for the continuation of analytic functions.
{"title":"Increasing stability for inverse acoustic source problems in the time domain","authors":"Chun Liu , Suliang Si , Guanghui Hu , Bo Zhang","doi":"10.1016/j.jde.2026.114114","DOIUrl":"10.1016/j.jde.2026.114114","url":null,"abstract":"<div><div>This paper is concerned with the inverse source problems for the acoustic wave equation in the full space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, where the source term is compactly supported in both time and spatial variables. The main goal is to investigate increasing stability for the wave equation in terms of the interval length of given parameters (e.g., frequency bandwith of the temporal component of the source function). We establish increasing stability estimates of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm of the source function by using only the Dirichlet boundary data. Our method relies on the Huygens' principle, the Fourier transform and explicit bounds for the continuation of analytic functions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"461 ","pages":"Article 114114"},"PeriodicalIF":2.3,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980596","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}
Pub Date : 2026-04-25Epub Date: 2026-01-14DOI: 10.1016/j.jde.2026.114108
Zijin Li , Ning Liu , Taoran Zhou
We consider the generalized Leray's problem with the Navier-slip boundary condition in an infinite pipe . We show that if the flux Φ of the solution is no larger than a critical value that is independent with the friction ratio of the Navier-slip boundary condition, the solution to the problem must be the parallel Poiseuille flow with the given flux. Compared with known related 3D results, this seems to be the first conclusion with the size of critical flux being uniform with the friction ratio , and it is surprising since the prescribed uniqueness breaks down immediately when , even if .
Our proof relies primarily on a refined gradient estimate of the Poiseuille flow with the Navier-slip boundary condition. Additionally, we prove the critical flux provided that Σ is a unit disk.
{"title":"A refined uniqueness result of Leray's problem in an infinite-long pipe with the Navier-slip boundary","authors":"Zijin Li , Ning Liu , Taoran Zhou","doi":"10.1016/j.jde.2026.114108","DOIUrl":"10.1016/j.jde.2026.114108","url":null,"abstract":"<div><div>We consider the generalized Leray's problem with the Navier-slip boundary condition in an infinite pipe <span><math><mi>D</mi><mo>=</mo><mi>Σ</mi><mo>×</mo><mi>R</mi></math></span>. We show that if the flux Φ of the solution is no larger than a critical value that is <em>independent with the friction ratio</em> of the Navier-slip boundary condition, the solution to the problem must be the parallel Poiseuille flow with the given flux. Compared with known related 3D results, this seems to be the first conclusion with the size of critical flux being uniform with the friction ratio <span><math><mi>α</mi><mo>∈</mo><mo>]</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>]</mo></math></span>, and it is surprising since the prescribed uniqueness breaks down immediately when <span><math><mi>α</mi><mo>=</mo><mn>0</mn></math></span>, even if <span><math><mi>Φ</mi><mo>=</mo><mn>0</mn></math></span>.</div><div>Our proof relies primarily on a refined gradient estimate of the Poiseuille flow with the Navier-slip boundary condition. Additionally, we prove the critical flux <span><math><msub><mrow><mi>Φ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≥</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>16</mn></mrow></mfrac></math></span> provided that Σ is a unit disk.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"461 ","pages":"Article 114108"},"PeriodicalIF":2.3,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980653","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号