Journal of Mathematical Analysis and Applications最新文献

{"title":"On the spectra of planar self-affine measures with p digits","authors":"Jian Cao","doi":"10.1016/j.jmaa.2025.129587","DOIUrl":"10.1016/j.jmaa.2025.129587","url":null,"abstract":"<div><div>For a prime number <span><math><mi>p</mi><mo>≥</mo><mn>3</mn></math></span>, let <span><math><mi>A</mi><mo>∈</mo><msub><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>Z</mi><mo>)</mo></math></span> be an expanding matrix and let <span><math><mi>B</mi><mo>⊂</mo><msup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> be a <em>p</em>-element digit set satisfying that<span><span><span><math><mrow><mi>Z</mi><mo>(</mo><msub><mrow><mover><mrow><mi>δ</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mi>B</mi></mrow></msub><mo>)</mo><mo>=</mo><munderover><mo>⋃</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></munderover><mo>(</mo><mfrac><mrow><mi>j</mi></mrow><mrow><mi>p</mi></mrow></mfrac><mrow><mo>(</mo><mtable><mtr><mtd><mi>ω</mi></mtd></mtr><mtr><mtd><mi>ρ</mi></mtd></mtr></mtable><mo>)</mo></mrow><mo>+</mo><msup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>,</mo></mrow></math></span></span></span> where <span><math><mo>{</mo><mi>ρ</mi><mo>,</mo><mi>ω</mi><mo>}</mo><mo>⊂</mo><mo>{</mo><mn>1</mn><mo>,</mo><mo>⋯</mo><mo>,</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>}</mo></math></span> and <span><math><mi>gcd</mi><mo>⁡</mo><mo>(</mo><mi>ρ</mi><mo>,</mo><mi>ω</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></span>. Here <span><math><mi>Z</mi><mo>(</mo><msub><mrow><mover><mrow><mi>δ</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mi>B</mi></mrow></msub><mo>)</mo></math></span> denotes the zero set of the function <span><math><msub><mrow><mover><mrow><mi>δ</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mi>B</mi></mrow></msub></math></span>. The associated self-affine measure <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>A</mi><mo>,</mo><mi>B</mi></mrow></msub></math></span> is generated by the iterated function system (IFS):<span><span><span><math><msub><mrow><mo>{</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>:</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>,</mo><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>}</mo></mrow><mrow><mi>b</mi><mo>∈</mo><mi>B</mi></mrow></msub><mo>.</mo></math></span></span></span> In this paper, some equivalent conditions for the self-affine measure <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>A</mi><mo>,</mo><mi>B</mi></mrow></msub></math></span> to be spectral are obtained. This extends the result of An, He and Tao <span><span>[2]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129587"},"PeriodicalIF":1.2,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global gradient estimates for solutions of parabolic equations with nonstandard growth","authors":"Rakesh Arora ,&nbsp;Sergey Shmarev","doi":"10.1016/j.jmaa.2025.129582","DOIUrl":"10.1016/j.jmaa.2025.129582","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We study how the smoothness of the initial datum and the free term affect the global regularity properties of solutions to the Dirichlet problem for the class of parabolic equations of &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&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;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;-Laplace type&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&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;msub&gt;&lt;mrow&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&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;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Q&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;Ω&lt;/mi&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;mi&gt;T&lt;/mi&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; with the nonlinear source &lt;span&gt;&lt;math&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&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;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&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;mo&gt;(&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&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;s&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. It is proven the existence of a solution such that if &lt;span&gt;&lt;math&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&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;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; for some &lt;span&gt;&lt;math&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mi&gt;max&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;max&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;z&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, then the gradient preserves the initial order of integrability in time, gains global higher integrability, and the solution acquires the second-order regularity in the following sense:&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&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;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mrow&gt;&lt;mtext&gt; for a.e. &lt;/mtext&gt;&lt;mi&gt;t&lt;/mi&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;mi&gt;T&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mrow&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;mo&gt;(&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Q&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;mrow&gt;&lt;mtext&gt; for any &lt;/mtext&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;)&lt;/","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129582"},"PeriodicalIF":1.2,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143834494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Carleman estimates for an N− dimensional plate equation with clamped boundary conditions and applications","authors":"Alex Imba ,&nbsp;Alberto Mercado","doi":"10.1016/j.jmaa.2025.129583","DOIUrl":"10.1016/j.jmaa.2025.129583","url":null,"abstract":"<div><div>In this paper, we establish a new global Carleman estimate for the Euler-Bernoulli plate operator acting in a bounded domain of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> with <span><math><mi>N</mi><mo>⩾</mo><mn>2</mn></math></span>, in which clamped boundary conditions have been imposed. We obtain a weighted estimate with observations in part of the boundary. As an application of the Carleman inequality, we obtain a Lipschitz stability result for the inverse problem of recovering the spatial part of the source term of the system from boundary measurements at any arbitrary positive time.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129583"},"PeriodicalIF":1.2,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143844734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On eigenvibrations of branched structures with heterogeneous mass density","authors":"Yuriy Golovaty ,&nbsp;Delfina Gómez ,&nbsp;Maria-Eugenia Pérez-Martínez","doi":"10.1016/j.jmaa.2025.129586","DOIUrl":"10.1016/j.jmaa.2025.129586","url":null,"abstract":"<div><div>We deal with a spectral problem for the Laplace-Beltrami operator posed on a stratified set Ω which is composed of smooth surfaces joined along a line <em>γ</em>, <em>the junction</em>. Through this junction we impose the Kirchhoff-type vertex conditions, which imply the continuity of the solutions and some balance for normal derivatives, and Neumann conditions on the rest of the boundary of the surfaces. Assuming that the density is <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mi>m</mi></mrow></msup><mo>)</mo></math></span> along small bands of width <span><math><mi>O</mi><mo>(</mo><mi>ε</mi><mo>)</mo></math></span>, which collapse into the line <em>γ</em> as <em>ε</em> tends to zero, and it is <span><math><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span> outside these bands, we address the asymptotic behavior, as <span><math><mi>ε</mi><mo>→</mo><mn>0</mn></math></span>, of the eigenvalues and of the corresponding eigenfunctions for a parameter <span><math><mi>m</mi><mo>≥</mo><mn>1</mn></math></span>. We also study the asymptotics for high frequencies when <span><math><mi>m</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129586"},"PeriodicalIF":1.2,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the regularity of the solutions of the Hall-magnetohydrodynamics system","authors":"Mohammad Mahabubur Rahman","doi":"10.1016/j.jmaa.2025.129584","DOIUrl":"10.1016/j.jmaa.2025.129584","url":null,"abstract":"<div><div>Due to the lack of sufficient dissipation and diffusion in controlling all nonlinear terms including the Hall term, the global regularity of the 3-D Hall-magnetohydrodynamics (Hall-MHD) system remains an outstanding open problem. Establishing the global regularity criterion in terms of <span><math><mi>∇</mi><msub><mrow><mi>b</mi></mrow><mrow><mi>h</mi></mrow></msub></math></span> is also challenging due to the inherent complexities introduced by the highly nonlinear Hall term, as described in <span><span>[29, Remark 2.3(1)]</span></span>. However, we obtain several regularity results, including for <span><math><mi>∇</mi><msub><mrow><mi>b</mi></mrow><mrow><mi>h</mi></mrow></msub></math></span>, in both the 3-D Hall equation and 3-D Hall-MHD system, along with key cancellations that might play an important role in gaining a better understanding of nonlinear phenomena for the Hall-MHD system.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129584"},"PeriodicalIF":1.2,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143856112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Transition threshold for the 2-D Couette flow in whole space via Green's function","authors":"Gaofeng Wang ,&nbsp;Weike Wang","doi":"10.1016/j.jmaa.2025.129585","DOIUrl":"10.1016/j.jmaa.2025.129585","url":null,"abstract":"<div><div>In this paper, we investigate the transition threshold problem concerning the 2-D Navier-Stokes equations in the context of Couette flow <span><math><mo>(</mo><mi>y</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></span> at high Reynolds number <em>Re</em> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. By utilizing Green's function estimates for the linearized equations around Couette flow, we initially establish refined dissipation estimates for the linearized Navier-Stokes equations with a precise decay rate <span><math><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>t</mi><mo>)</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span>. As an application, we prove that if the initial perturbation of vorticity satisfies<span><span><span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>ω</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>∩</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></mrow></msub><mo>≤</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub><msup><mrow><mi>ν</mi></mrow><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></msup></math></span></span></span> for some small constant <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> independent of the viscosity <em>ν</em>, then we can reach the conclusion that the vorticity remains within <span><math><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>ν</mi></mrow><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></msup><mo>)</mo></mrow></math></span> of the Couette flow.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129585"},"PeriodicalIF":1.2,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143825859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cauchy integral formulae for solutions to polynomial Dirac equations with α-weight","authors":"Shuoxing He,&nbsp;Xiaojing Du,&nbsp;Yonghong Xie","doi":"10.1016/j.jmaa.2025.129577","DOIUrl":"10.1016/j.jmaa.2025.129577","url":null,"abstract":"<div><div>Firstly, the Cauchy integral formula for solutions to polynomial Dirac equations with <em>α</em>-weight is obtained by constructing a new kernel function. Subsequently, the relationship between the solutions to polynomial Dirac equations with <em>α</em>-weight and <em>k</em>-monogenic functions with <em>α</em>-weight is established. Based on this relationship, the corresponding Cauchy integral formula for solutions to polynomial Dirac equations with <em>α</em>-weight is presented.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129577"},"PeriodicalIF":1.2,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143825858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weighted Triebel-Lizorkin spaces with variable smoothness and integrability","authors":"Shengrong Wang ,&nbsp;Pengfei Guo ,&nbsp;Jingshi Xu","doi":"10.1016/j.jmaa.2025.129578","DOIUrl":"10.1016/j.jmaa.2025.129578","url":null,"abstract":"<div><div>In this paper, we introduce the weighted Triebel-Lizorkin spaces of variable integral, smooth and summation exponents with variable Muckenhoupt weights. To make these spaces definite, we provide the weighted vector-valued convolution inequality and the Fourier multiplier theorem on these spaces. We then obtain a characterization of these spaces via approximation by analytic functions. Furthermore, we obtain embeddings, the lifting property, and duality of these spaces, respectively. Finally, we study the real interpolation in these spaces.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129578"},"PeriodicalIF":1.2,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143844733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analytic normalization of analytically integrable periodic difference system","authors":"Lazhan Yang,&nbsp;Ying Yang,&nbsp;Zhihua Ren","doi":"10.1016/j.jmaa.2025.129579","DOIUrl":"10.1016/j.jmaa.2025.129579","url":null,"abstract":"<div><div>The main purpose of this paper is to study the normal form and the existence of analytic normalization for the completely analytically integrable periodic difference system. The study extends the normal form theory of analytically integrable autonomous difference systems near a singularity to periodic difference systems.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129579"},"PeriodicalIF":1.2,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143825431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Study of multi-term fractional delay differential equations involving Caputo-fractional derivative","authors":"Iram Iqbal ,&nbsp;Fatiha Moh. Alsammak ,&nbsp;Mashaer Alsaeedi ,&nbsp;Mhassen E.E. Dalam ,&nbsp;Bilal Iqbal","doi":"10.1016/j.jmaa.2025.129563","DOIUrl":"10.1016/j.jmaa.2025.129563","url":null,"abstract":"<div><div>The aim of this paper is to produce some necessary conditions to exhibit the existence of solutions for the multi-term delay fractional boundary value problems subject to the periodic/anti-periodic boundary conditions in setting of ♭-metric spaces. In this regard we obtain the fixed-point results for <span><math><mi>F</mi></math></span>-type mappings that satisfy specific contractive criteria and have less limitations put on function <span><math><mi>F</mi></math></span> and then prove the existence results with the aid of obtained fixed point results.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129563"},"PeriodicalIF":1.2,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143820545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}