发布求助
文献互助 智能选刊 最新文献

Journal of Evolution Equations最新文献

筛选
英文 中文
Existence and convergence of the length-preserving elastic flow of clamped curves 夹紧曲线的保长弹性流的存在性和收敛性
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-07-02 DOI: 10.1007/s00028-024-00988-1
Fabian Rupp, Adrian Spener
{"title":"Existence and convergence of the length-preserving elastic flow of clamped curves","authors":"Fabian Rupp, Adrian Spener","doi":"10.1007/s00028-024-00988-1","DOIUrl":"https://doi.org/10.1007/s00028-024-00988-1","url":null,"abstract":"<p>We study the evolution of curves with fixed length and clamped boundary conditions moving by the negative <span>(L^2)</span>-gradient flow of the elastic energy. For any initial curve lying merely in the energy space we show existence and parabolic smoothing of the solution. Applying previous results on long-time existence and proving a constrained Łojasiewicz–Simon gradient inequality we furthermore show convergence to a critical point as time tends to infinity.\u0000</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"16 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141526882","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}
引用次数: 0
Algebraic decay rates for 3D Navier–Stokes and Navier–Stokes–Coriolis equations in $$ dot{H}^{frac{1}{2}}$$ 三维纳维-斯托克斯方程和纳维-斯托克斯-科里奥利方程在 $$ dot{H}^{frac{1}{2}}$ 中的代数衰减率
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-06-29 DOI: 10.1007/s00028-024-00991-6
Masahiro Ikeda, Leonardo Kosloff, César J. Niche, Gabriela Planas
{"title":"Algebraic decay rates for 3D Navier–Stokes and Navier–Stokes–Coriolis equations in $$ dot{H}^{frac{1}{2}}$$","authors":"Masahiro Ikeda, Leonardo Kosloff, César J. Niche, Gabriela Planas","doi":"10.1007/s00028-024-00991-6","DOIUrl":"https://doi.org/10.1007/s00028-024-00991-6","url":null,"abstract":"<p>An algebraic upper bound for the decay rate of solutions to the Navier–Stokes and Navier–Stokes–Coriolis equations in the critical space <span>(dot{H} ^{frac{1}{2}} (mathbb {R}^3))</span> is derived using the Fourier splitting method. Estimates are framed in terms of the decay character of initial data, leading to solutions with algebraic decay and showing in detail the roles played by the linear and nonlinear parts. The proof is carried on purely in the critical space, as no <span>(L^2 (mathbb {R}^3))</span> estimates are available for the solution. This is the first instance in which such a method is used for obtaining decay bounds in a critical space for a nonlinear equation.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"122 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503813","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}
引用次数: 0
An interpolation inequality and its applications to stability of fractional resolvent families 插值不等式及其在分数解析族稳定性中的应用
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-06-28 DOI: 10.1007/s00028-024-00990-7
Jie Mei, Miao Li
{"title":"An interpolation inequality and its applications to stability of fractional resolvent families","authors":"Jie Mei, Miao Li","doi":"10.1007/s00028-024-00990-7","DOIUrl":"https://doi.org/10.1007/s00028-024-00990-7","url":null,"abstract":"<p>In this paper, we prove an interpolation inequality on Riemann–Liouville fractional integrals and then use it to study the strong stability and semi-uniform stability of fractional resolvent families of order <span>(0&lt;alpha &lt;2)</span>. Let <i>A</i> denote the generator of a bounded fractional resolvent family. We show that if <span>(sigma (A)cap (textrm{i}{mathbb {R}})^alpha )</span> is countable and <span>(sigma _r(A) cap (textrm{i}{mathbb {R}})^alpha =varnothing )</span>, then the bounded fractional resolvent family is strongly stable. And the semi-uniform stability of the fractional resolvent family is equivalent to <span>(sigma (A)cap (textrm{i}{mathbb {R}})^alpha =varnothing )</span>. Moreover, the relation between decay rates of semi-uniform stability and growth of the resolvent of <i>A</i> along <span>((textrm{i}{mathbb {R}})^alpha )</span> is given.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"10 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503816","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}
引用次数: 0
Stability of rotating liquid drops with surface tension 具有表面张力的旋转液滴的稳定性
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-06-25 DOI: 10.1007/s00028-024-00986-3
Keiichi Watanabe
{"title":"Stability of rotating liquid drops with surface tension","authors":"Keiichi Watanabe","doi":"10.1007/s00028-024-00986-3","DOIUrl":"https://doi.org/10.1007/s00028-024-00986-3","url":null,"abstract":"<p>The aim of this paper is to investigate the stability of a stationary solution of free boundary problems of the incompressible Navier–Stokes equations in a three-dimensional bounded domain with surface tension. More precisely, this article proves that if the initial angular momentum is sufficiently small and if the initial configuration is sufficiently close to equilibrium, then there exists a global classical solution that converges exponentially fast to a uniform rigid rotation of the liquid as <span>(t rightarrow infty )</span> with respect to a certain axis. The proof of the <i>unique</i> existence of a stationary solution is also given.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"83 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503815","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}
引用次数: 0
Fujita exponent for non-local parabolic equation involving the Hardy–Leray potential 涉及哈代-勒雷势的非局部抛物方程的藤田指数
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-06-22 DOI: 10.1007/s00028-024-00984-5
Boumediene Abdellaoui, Giovanni Siclari, Ana Primo
{"title":"Fujita exponent for non-local parabolic equation involving the Hardy–Leray potential","authors":"Boumediene Abdellaoui, Giovanni Siclari, Ana Primo","doi":"10.1007/s00028-024-00984-5","DOIUrl":"https://doi.org/10.1007/s00028-024-00984-5","url":null,"abstract":"<p>In this paper, we analyse the existence and non-existence of non-negative solutions to a non-local parabolic equation with a Hardy–Leray-type potential. More precisely, we consider the problem </p><span>$$begin{aligned} {left{ begin{array}{ll} (w_t-Delta w)^s=frac{lambda }{|x|^{2s}} w+w^p +f, &amp;{}quad text {in }mathbb {R}^Ntimes (0,+infty ), w(x,t)=0, &amp;{}quad text {in }mathbb {R}^Ntimes (-infty ,0], end{array}right. } end{aligned}$$</span><p>where <span>(N&gt; 2s)</span>, <span>(0&lt;s&lt;1)</span> and <span>(0&lt;lambda &lt;Lambda _{N,s})</span>, the optimal constant in the fractional Hardy–Leray inequality. In particular, we show the existence of a critical existence exponent <span>(p_{+}(lambda , s))</span> and of a Fujita-type exponent <span>(F(lambda ,s))</span> such that the following holds:</p><ul>\u0000<li>\u0000<p>Let <span>(p&gt;p_+(lambda ,s))</span>. Then there are not any non-negative supersolutions.</p>\u0000</li>\u0000<li>\u0000<p>Let <span>(p&lt;p_+(lambda ,s))</span>. Then there exist local solutions, while concerning global solutions we need to distinguish two cases:</p><ul>\u0000<li>\u0000<p>Let <span>( 1&lt; ple F(lambda ,s))</span>. Here we show that a weighted norm of any positive solution blows up in finite time.</p>\u0000</li>\u0000<li>\u0000<p>Let <span>(F(lambda ,s)&lt;p&lt;p_+(lambda ,s))</span>. Here we prove the existence of global solutions under suitable hypotheses.</p>\u0000</li>\u0000</ul>\u0000</li>\u0000</ul>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"23 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On $$L^2$$ decay of weak solutions of several incompressible fluid models 论若干不可压缩流体模型弱解的 $$L^2$$ 衰减
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-06-22 DOI: 10.1007/s00028-024-00985-4
Huan Yu
{"title":"On $$L^2$$ decay of weak solutions of several incompressible fluid models","authors":"Huan Yu","doi":"10.1007/s00028-024-00985-4","DOIUrl":"https://doi.org/10.1007/s00028-024-00985-4","url":null,"abstract":"<p>In this paper, we are concerned with <span>(L^2)</span> decay of weak solutions of several well-known incompressible fluid models, such as the n-dimensional (<span>(nge 2)</span>) Navier–Stokes equations with fractional hyperviscosity, the three-dimensional convective Brinkman–Forchheimer equations and the generalized SQG equation. A new approach, different from the classical Fourier splitting method develpoed by Schonbek (Commun Partial Differ Equ 11:733–763, 1986) and the spectral representation technique by Kajikiya and Miyakawa (Math Z 192:135-148,1986), is presented. By using the new approach, we can recover and improve some known decay results.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"54 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503817","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}
引用次数: 0
Vertical maximal functions on manifolds with ends 有端流形上的垂直最大函数
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-06-09 DOI: 10.1007/s00028-024-00981-8
Himani Sharma, Adam Sikora
{"title":"Vertical maximal functions on manifolds with ends","authors":"Himani Sharma, Adam Sikora","doi":"10.1007/s00028-024-00981-8","DOIUrl":"https://doi.org/10.1007/s00028-024-00981-8","url":null,"abstract":"<p>We consider the setting of manifolds with ends which are obtained by compact perturbation (gluing) of ends of the form <span>({mathbb {R}}^{n_i}times {mathcal {M}}_i)</span>. We investigate the family of vertical resolvent <span>({sqrt{t}nabla (1+tDelta )^{-m}}_{t&gt;0})</span>, where <span>(mge 1)</span>. We show that the family is uniformly continuous on all <span>(L^p)</span> for <span>(1le ~p~le ~min _{i}n_i)</span>. Interestingly, this is a closed-end condition in the considered setting. We prove that the corresponding maximal function is bounded in the same range except that it is only weak-type (1, 1) for <span>(p=1)</span>. The Fefferman-Stein vector-valued maximal function is again of weak-type (1, 1) but bounded if and only if <span>(1&lt;p&lt;min _{i}n_i)</span>, and not at <span>(p=min _{i}n_i)</span>.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"23 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503819","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}
引用次数: 0
Semilinear damped wave equations on the Heisenberg group with initial data from Sobolev spaces of negative order 海森堡群上的半线性阻尼波方程与负阶索博列夫空间的初始数据
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-06-09 DOI: 10.1007/s00028-024-00976-5
Aparajita Dasgupta, Vishvesh Kumar, Shyam Swarup Mondal, Michael Ruzhansky
{"title":"Semilinear damped wave equations on the Heisenberg group with initial data from Sobolev spaces of negative order","authors":"Aparajita Dasgupta, Vishvesh Kumar, Shyam Swarup Mondal, Michael Ruzhansky","doi":"10.1007/s00028-024-00976-5","DOIUrl":"https://doi.org/10.1007/s00028-024-00976-5","url":null,"abstract":"<p>In this paper, we focus on studying the Cauchy problem for semilinear damped wave equations involving the sub-Laplacian <span>(mathcal {L})</span> on the Heisenberg group <span>(mathbb {H}^n)</span> with power type nonlinearity <span>(|u|^p)</span> and initial data taken from Sobolev spaces of negative order homogeneous Sobolev space <span>(dot{H}^{-gamma }_{mathcal {L}}(mathbb {H}^n), gamma &gt;0)</span>, on <span>(mathbb {H}^n)</span>. In particular, in the framework of Sobolev spaces of negative order, we prove that the critical exponent is the exponent <span>(p_{text {crit}}(Q, gamma )=1+frac{4}{Q+2gamma },)</span> for <span>(gamma in (0, frac{Q}{2}))</span>, where <span>(Q:=2n+2)</span> is the homogeneous dimension of <span>(mathbb {H}^n)</span>. More precisely, we establish</p><ul>\u0000<li>\u0000<p>A global-in-time existence of small data Sobolev solutions of lower regularity for <span>(p&gt;p_{text {crit}}(Q, gamma ))</span> in the energy evolution space;</p>\u0000</li>\u0000<li>\u0000<p>A finite time blow-up of weak solutions for <span>(1&lt;p&lt;p_{text {crit}}(Q, gamma ))</span> under certain conditions on the initial data by using the test function method.</p>\u0000</li>\u0000</ul><p> Furthermore, to precisely characterize the blow-up time, we derive sharp upper bound and lower bound estimates for the lifespan in the subcritical case.\u0000</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"23 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503820","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}
引用次数: 0
On the second boundary value problem for a class of fully nonlinear flow III 关于一类全非线性流动的第二边界值问题 III
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-06-09 DOI: 10.1007/s00028-024-00983-6
Chong Wang, Rongli Huang, Jiguang Bao
{"title":"On the second boundary value problem for a class of fully nonlinear flow III","authors":"Chong Wang, Rongli Huang, Jiguang Bao","doi":"10.1007/s00028-024-00983-6","DOIUrl":"https://doi.org/10.1007/s00028-024-00983-6","url":null,"abstract":"<p>We study the solvability of the second boundary value problem of the Lagrangian mean curvature equation arising from special Lagrangian geometry. By the parabolic method, we obtain the existence and uniqueness of the smooth uniformly convex solution, which generalizes the Brendle–Warren’s theorem about minimal Lagrangian diffeomorphism in Euclidean metric space.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"32 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141526883","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}
引用次数: 0
Dispersive decay bound of small data solutions to Kawahara equation in a finite time scale 有限时间尺度内川原方程小数据解的分散衰减约束
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-05-24 DOI: 10.1007/s00028-024-00980-9
Jongwon Lee
{"title":"Dispersive decay bound of small data solutions to Kawahara equation in a finite time scale","authors":"Jongwon Lee","doi":"10.1007/s00028-024-00980-9","DOIUrl":"https://doi.org/10.1007/s00028-024-00980-9","url":null,"abstract":"<p>In this article, we prove that small localized data yield solutions to Kawahara-type equations which have linear dispersive decay on a finite time scale depending on the size of the initial data. We use the similar method used by Ifrim and Tataru to derive the dispersive decay bound of the solutions to the KdV equation, with some steps being simpler. This result is expected to be the first result of the small data global bounds of the fifth-order dispersive equations with quadratic nonlinearity.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"11 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141147682","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}
引用次数: 0
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信