Journal of Differential Equations最新文献

{"title":"Elliptic equations in divergence form with zero mass and critical exponential growth","authors":"J.C. de Albuquerque ,&nbsp;J. Carvalho ,&nbsp;E.D. Silva","doi":"10.1016/j.jde.2025.113743","DOIUrl":"10.1016/j.jde.2025.113743","url":null,"abstract":"<div><div>In this work, we consider a class of elliptic equations in divergence form with zero mass, involving weight functions that are not necessarily symmetric and nonlinearities satisfying critical exponential growth. For this purpose, we introduce a weighted Trudinger-Moser type inequality. We prove the existence of nonnegative least energy solutions and investigate their qualitative properties, including asymptotic behavior, growth estimates, regularity results, and the existence of strictly positive solutions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113743"},"PeriodicalIF":2.3,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144989805","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":"Sufficient conditions for the n-dimensional real Jacobian conjecture","authors":"Changjian Liu ,&nbsp;Yuzhou Tian","doi":"10.1016/j.jde.2025.113750","DOIUrl":"10.1016/j.jde.2025.113750","url":null,"abstract":"<div><div>The real Jacobian conjecture, proposed by Randall in 1983, asserts that a polynomial map <span><math><mi>F</mi><mo>=</mo><mrow><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow><mo>:</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> such that <span><math><mi>det</mi><mo>⁡</mo><mi>D</mi><mi>F</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>≠</mo><mn>0</mn></math></span> for all <span><math><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> is injective. However, this conjecture is disproven by Pinchuk's counterexample.</div><div>This investigation mainly consists of two parts. Firstly, we use the qualitative theory of dynamical systems to give an alternative proof of the polynomial version of the <em>n</em>-dimensional Hadamard's theorem. Secondly, we present some algebraic sufficient conditions for the <em>n</em>-dimensional real Jacobian conjecture. Our results not only extend the main result of [J. Differential Equations <strong>260</strong> (2016), 5250-5258] to quasi-homogeneous type, but also generalize it from <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> to <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. As a coproduct of our proof process, we solve an open problem formulated by Braun, Giné and Llibre in [J. Differential Equations <strong>260</strong> (2016), 5250-5258].</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"446 ","pages":"Article 113750"},"PeriodicalIF":2.3,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988061","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 asymptotic of the Mullins-Sekerka and the area-preserving curvature flow in the planar flat torus","authors":"Vedansh Arya ,&nbsp;Daniele De Gennaro ,&nbsp;Anna Kubin","doi":"10.1016/j.jde.2025.113755","DOIUrl":"10.1016/j.jde.2025.113755","url":null,"abstract":"<div><div>We study the asymptotic behavior of flat flow solutions to the periodic and planar two-phase Mullins-Sekerka flow and area-preserving curvature flow. We show that flat flows converge to either a finite union of equally sized disjoint disks or to a finite union of disjoint strips or to the complement of these configurations exponentially fast. A key ingredient in our approach is the derivation of a sharp quantitative Alexandrov inequality for periodic smooth sets.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113755"},"PeriodicalIF":2.3,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144989806","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":"Spreading dynamics of a nonlocal diffusive model with a free boundary","authors":"Lei Li ,&nbsp;Mingxin Wang","doi":"10.1016/j.jde.2025.113741","DOIUrl":"10.1016/j.jde.2025.113741","url":null,"abstract":"<div><div>We study the spreading speed and asymptotic behavior of the solution to a nonlocal diffusive model with a free boundary. First, we construct a suitable lower solution to determine the exact finite spreading speed of the free boundary <span><math><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span>, which is also the asymptotic spreading speed of the population density <span><math><mi>u</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></span>. Then, we investigate the asymptotic behavior of the level set <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math></span> of <span><math><mi>u</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></span> and find an intriguing propagation phenomenon. Specifically, as <span><math><mi>t</mi><mo>→</mo><mo>∞</mo></math></span>, for large <em>λ</em>, the infimum of <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math></span> converges to a unique constant determined by a positive steady state, while the infimum for small <em>λ</em> and the supremum for all considered <em>λ</em> share the same spreading speed as that of <span><math><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span>. Finally, when the spreading speed is infinite, a phenomenon known as accelerated spreading, we employ two lower solutions to derive the rate of accelerated spreading and the asymptotic behavior of <span><math><mi>u</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></span> for algebraically decaying kernels.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"449 ","pages":"Article 113741"},"PeriodicalIF":2.3,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932787","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 stability on the Caffarelli-Kohn-Nirenberg and Hardy-type inequalities and beyond","authors":"Yuxuan Zhou,&nbsp;Wenming Zou","doi":"10.1016/j.jde.2025.113738","DOIUrl":"10.1016/j.jde.2025.113738","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper, we establish several improved Caffarelli-Kohn-Nirenberg and Hardy-type inequalities. Our main results are divided into two parts.&lt;/div&gt;&lt;div&gt;In the first part, we consider the following Caffarelli-Kohn-Nirenberg inequality:&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&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;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&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;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is the sharp constant and &lt;span&gt;&lt;math&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; satisfy the relations:&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&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;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; We establish gradient stability of this inequality in both functional and critical settings, and we derive some functional properties of the stability constant. Building on the gradient stability, we also obtain several refined Sobolev-type embeddings involving weak Lebesgue norms for functions supported in general domains.&lt;/div&gt;&lt;div&gt;In the second part, we focus on various classical Hardy-type inequalities, including the standard Hardy inequality, the &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;-logarithmic Sobolev inequality with weights, the logarithmic Hardy inequality, the Hardy-Morrey inequality, the Hardy-Sobolev interpolati","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"450 ","pages":"Article 113738"},"PeriodicalIF":2.3,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144933087","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":"Stokes-Brinkman equations with diffusion and convection in thin tube structures","authors":"Antonio Gaudiello ,&nbsp;Grigory Panasenko","doi":"10.1016/j.jde.2025.113728","DOIUrl":"10.1016/j.jde.2025.113728","url":null,"abstract":"<div><div>The steady state Stokes-Brinkman equations coupled with a system of diffusion-convection equations in a thin tube structure is considered. The Brinkman term differs from zero only in small balls near the ends of the tubes. The boundary conditions are: given pressure and concentrations at the inflow and outflow of the tube structure, the no slip boundary condition on the lateral boundary for the fluid, and Neumann type condition on the lateral boundary for the diffusion-convection equations. In this paper, the existence, uniqueness, and stability of the solution to such a problem are proved. Moreover, some <em>a priori</em> norm-estimates depending on the small thickness of the tubes are also provided. This model is well suited to describing thrombosis in blood vessels.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"450 ","pages":"Article 113728"},"PeriodicalIF":2.3,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144933089","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":"Cancellation properties and unconditional well-posedness for fifth order modified KdV type equations with periodic boundary conditions","authors":"Takamori Kato ,&nbsp;Kotaro Tsugawa","doi":"10.1016/j.jde.2025.113736","DOIUrl":"10.1016/j.jde.2025.113736","url":null,"abstract":"<div><div>We prove the unconditional well-posedness result for fifth order modified KdV type equations in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mo>(</mo><mi>T</mi><mo>)</mo></math></span> when <span><math><mi>s</mi><mo>≥</mo><mn>3</mn><mo>/</mo><mn>2</mn></math></span>, which includes non-integrable cases. By the conservation laws, we also obtain the global well-posedness result when <span><math><mi>s</mi><mo>=</mo><mn>2</mn></math></span>, which also includes non-integrable cases. The main idea is to employ the normal form reduction and a kind of cancellation properties to deal with the derivative losses.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"450 ","pages":"Article 113736"},"PeriodicalIF":2.3,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144933088","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":"Polynomial differential systems with an arbitrary number of limit cycles surrounding a star node","authors":"Denis de Carvalho Braga ,&nbsp;Fabio Scalco Dias ,&nbsp;Jaume Llibre ,&nbsp;Luis Fernando Mello","doi":"10.1016/j.jde.2025.113740","DOIUrl":"10.1016/j.jde.2025.113740","url":null,"abstract":"<div><div>It is known that there are polynomial vector fields in the plane having an arbitrary number of limit cycles surrounding a focus, or a saddle, or a node. But until now this result was not proved for a star node. Here we consider polynomial vector fields in the plane with an equilibrium point of star node type, and we prove that there are such vector fields with an arbitrary number of limit cycles surrounding the star node.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"445 ","pages":"Article 113740"},"PeriodicalIF":2.3,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925788","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 for systems of 2-D wave equations with nonlinearity of the wave maps type in exterior domains","authors":"Hou Fei ,&nbsp;Yin Huicheng ,&nbsp;Yuan Meng","doi":"10.1016/j.jde.2025.113756","DOIUrl":"10.1016/j.jde.2025.113756","url":null,"abstract":"<div><div>In this paper, we solve the global Dirichelt boundary value problem for the system of 2-D wave maps type equations with the form <span><math><mo>□</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>I</mi></mrow></msup><mo>=</mo><munderover><mo>∑</mo><mrow><mi>J</mi><mo>,</mo><mi>K</mi><mo>,</mo><mi>L</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>M</mi></mrow></munderover><msub><mrow><mi>C</mi></mrow><mrow><mi>I</mi><mi>J</mi><mi>K</mi><mi>L</mi></mrow></msub><msup><mrow><mi>u</mi></mrow><mrow><mi>J</mi></mrow></msup><msub><mrow><mi>Q</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>K</mi></mrow></msup><mo>,</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>L</mi></mrow></msup><mo>)</mo></math></span> <span><math><mo>(</mo><mn>1</mn><mo>≤</mo><mi>I</mi><mo>≤</mo><mi>M</mi><mo>)</mo></math></span> and <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>f</mi><mo>,</mo><mi>g</mi><mo>)</mo><mo>=</mo><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>f</mi><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>g</mi><mo>−</mo><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></munderover><msub><mrow><mo>∂</mo></mrow><mrow><mi>j</mi></mrow></msub><mi>f</mi><msub><mrow><mo>∂</mo></mrow><mrow><mi>j</mi></mrow></msub><mi>g</mi></math></span> in exterior domain. By establishing some crucial classes of pointwise spacetime decay estimates for the small data solution <span><math><mi>u</mi><mo>=</mo><mo>(</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>,</mo><mo>⋅</mo><mo>⋅</mo><mo>⋅</mo><mo>,</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>M</mi></mrow></msup><mo>)</mo></math></span> and its derivatives, the global existence of <em>u</em> is shown.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113756"},"PeriodicalIF":2.3,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144933789","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":"Solvability and convergence results for the temperature and concentration field in incompressible Navier-Stokes equations with boundary conditions","authors":"Jianwei Hao ,&nbsp;Tomás Caraballo","doi":"10.1016/j.jde.2025.113735","DOIUrl":"10.1016/j.jde.2025.113735","url":null,"abstract":"<div><div>In this article, we consider a new and complicated coupled system consisting of the incompressible Navier-Stokes equations (NSEs) subject to boundary conditions, a fractional diffusion equation governing the concentration field, and an evolution equation describing the temperature field. Under mild assumptions, the existence of a mild solution to the coupled system is proved using a surjectivity result for weakly-weakly upper semicontinuous multivalued mappings, combined with a feedback iterative method and a temporally semi-discrete strategy. Additionally, we examine the asymptotic behavior of the solution sequence as the small parameter in the inertial term approaches zero, offering deeper insights into the limiting behavior and dynamic properties of the system.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"450 ","pages":"Article 113735"},"PeriodicalIF":2.3,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144921250","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}