Journal of Differential Equations最新文献

{"title":"Liouville-type theorems for steady Navier-Stokes system in a slab with Navier boundary conditions","authors":"Jingwen Han ,&nbsp;Yun Wang ,&nbsp;Chunjing Xie","doi":"10.1016/j.jde.2025.113556","DOIUrl":"10.1016/j.jde.2025.113556","url":null,"abstract":"<div><div>In this paper, the Liouville-type theorems for the steady Navier-Stokes system in a slab supplemented with Navier boundary conditions are investigated. Specifically, we prove that any bounded smooth solution must be zero if either the swirl or radial velocity is axisymmetric, or <span><math><mi>r</mi><msup><mrow><mi>u</mi></mrow><mrow><mi>r</mi></mrow></msup></math></span> decays to zero as <em>r</em> tends to infinity. When the velocity is not big in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-space, the general three-dimensional steady Navier-Stokes flow in a slab with the Navier boundary conditions must be a Poiseuille type flow. The key idea of the proof is to establish the Saint-Venant type estimates that characterize the growth of Dirichlet integral of nontrivial solutions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"443 ","pages":"Article 113556"},"PeriodicalIF":2.4,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144279244","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":"Very mild diffusion enhancement and singular sensitivity: Existence of bounded weak solutions in a two-dimensional chemotaxis-Navier–Stokes system","authors":"Tobias Black","doi":"10.1016/j.jde.2025.113555","DOIUrl":"10.1016/j.jde.2025.113555","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We consider an initial-boundary value problem for the chemotaxis-Navier–Stokes system&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&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;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; in a smoothly bounded domain &lt;span&gt;&lt;math&gt;&lt;m","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"443 ","pages":"Article 113555"},"PeriodicalIF":2.4,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144270696","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 optimal decay and propagation of regularity for the inhomogeneous Landau equation in (Lx∞ˆ∩Lxrˆ)Lv2 space","authors":"Hao-Guang Li","doi":"10.1016/j.jde.2025.113551","DOIUrl":"10.1016/j.jde.2025.113551","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We study the Cauchy problem for the inhomogeneous Landau equation with hard potentials and moderately soft potentials in &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mo&gt;∩&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; space with &lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. In perturbation framework, we establish the global existence and optimal time decay rate of the solution with initial datum &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mo&gt;∩&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; smallness, where &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; is the Riesz potential, &lt;span&gt;&lt;math&gt;&lt;mover&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/math&gt;&lt;/span&gt; is the Fourier-Hertz space equipped with the norm &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113551"},"PeriodicalIF":2.4,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144270684","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 of smooth solution to a non-conservative compressible two-fluid model in exterior domain","authors":"Qimeng Yang,&nbsp;Lei Yao","doi":"10.1016/j.jde.2025.113558","DOIUrl":"10.1016/j.jde.2025.113558","url":null,"abstract":"<div><div>In this paper, we consider the initial boundary value problem for a non-conservative compressible two-fluid model with Navier-slip boundary conditions in an exterior domain of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. We prove the global existence of smooth solution in a setting that the capillary pressure <span><math><mi>f</mi><mo>(</mo><msup><mrow><mi>α</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>ρ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo><mo>=</mo><msup><mrow><mi>P</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>−</mo><msup><mrow><mi>P</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>≠</mo><mn>0</mn></math></span>, where <em>f</em> is assumed to be a strictly decreasing function near the equilibrium of <span><math><msup><mrow><mi>α</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>ρ</mi></mrow><mrow><mo>−</mo></mrow></msup></math></span>, and prove that this assumption has a critical stabilization effect in the question. Furthermore, we establish the explicit decay rates of smooth solution to its equilibrium state.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"441 ","pages":"Article 113558"},"PeriodicalIF":2.4,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144271578","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":"Vanishing viscosity limit of the stationary Navier-Stokes equations with the Navier-slip boundary and its application","authors":"Xinghong Pan ,&nbsp;Jianfeng Zhao","doi":"10.1016/j.jde.2025.113548","DOIUrl":"10.1016/j.jde.2025.113548","url":null,"abstract":"<div><div>In this paper, we consider the vanishing viscosity limit of the stationary Navier-Stokes equations with the total Navier-slip boundary condition in a horizontally periodic strip. We will show that as the viscosity approaches to zero, there exist a sequence of solutions of the Navier-Stokes equations that approach that of the limiting Euler system. Moreover, we construct this sequence of solutions to keep the same cross-section flux with that of the limiting Euler, which is independent of the viscosity. Such construction of flux-conserved solutions is not easy to achieve in the case of the no-slip boundary condition. Due to the principle of the Prandtl-Batchelor theory, the limiting Euler solution can only be the Couette flow <span><math><mo>(</mo><mi>A</mi><mi>y</mi><mo>+</mo><mi>B</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></span> for some suitable constants <em>A</em> and <em>B</em>. The constant <em>A</em> is determined by the boundary condition and the constant <em>B</em> is determined by the given flux.</div><div>As an application, we can show the structure stability of any Couette flow <span><math><mo>(</mo><mi>A</mi><mi>y</mi><mo>+</mo><mi>B</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></span> for the stationary Navier-Stokes equations with fixed viscosity and suitably large flux when equipped with the total Navier-slip boundary condition.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"443 ","pages":"Article 113548"},"PeriodicalIF":2.4,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144270695","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 Vlasov-Yukawa-Boltzmann system without angular cutoff near vacuum","authors":"Xianshen Hu ,&nbsp;Linjie Xiong ,&nbsp;Wenzheng Zhu","doi":"10.1016/j.jde.2025.113518","DOIUrl":"10.1016/j.jde.2025.113518","url":null,"abstract":"<div><div>We investigate the global nonlinear stability of the non-cutoff Vlasov-Yukawa-Boltzmann (VYB) system with moderately soft potentials <span><math><mi>γ</mi><mo>+</mo><mn>2</mn><mi>s</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span> and all physically relevant singularity parameter <span><math><mi>s</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>. Building upon the foundational framework established in Chaturvedi's work [Ann. PDE, 7(2021), no.2, Paper No. 15, 104 pp.], we demonstrate the global nonlinear stability of the VYB system near vacuum by leveraging space-time weights and employing commuting vector fields to achieve integrable time decay for the nonlinear terms. This extends the existence result in Choi and Ha's work [Acta Math. Sci. Ser. B (Engl. Ed.) 35 (2015), no. 4, 887–905.] to angular non-cutoff cases.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"443 ","pages":"Article 113518"},"PeriodicalIF":2.4,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263882","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":"Corner direction flows of a compressible Stokes system","authors":"Jae Ryong Kweon,&nbsp;Tae Yeob Lee","doi":"10.1016/j.jde.2025.113549","DOIUrl":"10.1016/j.jde.2025.113549","url":null,"abstract":"<div><div>We study a compressible Stokes flow directed by a vector field that is tangential along the sides of a non-convex vertex and that has a jump across a subset in the domain. The jump restriction is imposed because the tangential flow lines along the corner sides may intersect in the interior of the domain. The solution of the transport equation directed by the vector field has a jump discontinuity across the interface curve emanating from the non-convex vertex. We construct a lifting vector handling the pressure gradient in the momentum equation and deal with the contact singularity at the point that the interface curve meets the boundary. We split from the velocity solution vector the corner singularities by the Lamé system. We finally show existence and piecewise regularity for a compressible Stokes system.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113549"},"PeriodicalIF":2.4,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263753","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 behaviour of non-radiative solution to the wave equations","authors":"Liang Li,&nbsp;Ruipeng Shen,&nbsp;Chenhui Wang,&nbsp;Lijuan Wei","doi":"10.1016/j.jde.2025.113547","DOIUrl":"10.1016/j.jde.2025.113547","url":null,"abstract":"<div><div>In this work we consider weakly non-radiative solutions to both linear and non-linear wave equations. We first characterize all weakly non-radiative free waves, without the radial assumption. Then in dimension 3 we show that the asymptotic behaviours of non-radiative solutions to a wide range of nonlinear wave equations are similar to those of non-radiative free waves. This generalizes the already known results about radial solutions to the non-radial case.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"441 ","pages":"Article 113547"},"PeriodicalIF":2.4,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144261807","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":"Well-posedness of stochastic chemotaxis system","authors":"Yunfeng Chen ,&nbsp;Jianliang Zhai ,&nbsp;Tusheng Zhang","doi":"10.1016/j.jde.2025.113531","DOIUrl":"10.1016/j.jde.2025.113531","url":null,"abstract":"<div><div>In this paper, we establish the existence and uniqueness of solutions of elliptic-parabolic stochastic Keller-Segel systems. The solution is obtained through a carefully designed localization procedure together with some a priori estimates. Both noise of linear growth and nonlinear noise are considered. The <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> Itô formula plays an important role.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"442 ","pages":"Article 113531"},"PeriodicalIF":2.4,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144254904","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 a coupled-physics transmission eigenvalue problem and its spectral properties with applications","authors":"Huaian Diao ,&nbsp;Hongyu Liu ,&nbsp;Qingle Meng ,&nbsp;Li Wang","doi":"10.1016/j.jde.2025.113508","DOIUrl":"10.1016/j.jde.2025.113508","url":null,"abstract":"<div><div>In this paper, we investigate a transmission eigenvalue problem that couples the principles of acoustics and elasticity. This problem naturally arises when studying fluid-solid interactions and constructing bubbly-elastic structures to create metamaterials. We uncover intriguing local geometric structures of the transmission eigenfunctions near the corners of the domains, under typical regularity conditions. As applications, we present novel unique identifiability and visibility results for an inverse problem associated with an acoustoelastic system, which hold practical significance.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"441 ","pages":"Article 113508"},"PeriodicalIF":2.4,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144254785","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}