Long time behavior of solutions of an electroconvection model in $${\mathbb {R}}^2$$

IF 1.1 3区数学 Q1 MATHEMATICS Journal of Evolution Equations Pub Date : 2024-02-10 DOI:10.1007/s00028-024-00944-z

引用次数: 0

Abstract

We consider a two dimensional electroconvection model which consists of a nonlinear and nonlocal system coupling the evolutions of a charge distribution and a fluid. We show that the solutions decay in time in $L^2({{\mathbb {R}}}^2)$ at the same sharp rate as the linear uncoupled system. This is achieved by proving that the difference between the nonlinear and linear evolution decays at a faster rate than the linear evolution. In order to prove the sharp $L^2$ decay we establish bounds for decay in $H^2({{\mathbb {R}}}^2)$ and a logarithmic growth in time of a quadratic moment of the charge density.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

电对流模型解在 $${mathbb {R}}^2$ 中的长时间行为

摘要我们考虑了一个二维电对流模型，它由一个非线性和非局部系统组成，耦合了电荷分布和流体的演化。我们证明，解在 $L^2({{\mathbb {R}}^2)$ 中的时间衰减速率与线性非耦合系统相同。这是通过证明非线性演化与线性演化之间的差值以比线性演化更快的速度衰减来实现的。为了证明$L^2$的急剧衰减，我们建立了$H^2({{/\mathbb {R}}^2)$ 的衰减和电荷密度二次矩的时间对数增长的边界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

来源期刊

Journal of Evolution Equations 数学-数学

CiteScore

2.30

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Evolution Equations (JEE) publishes high-quality, peer-reviewed papers on equations dealing with time dependent systems and ranging from abstract theory to concrete applications. Research articles should contain new and important results. Survey articles on recent developments are also considered as important contributions to the field. Particular topics covered by the journal are: Linear and Nonlinear Semigroups Parabolic and Hyperbolic Partial Differential Equations Reaction Diffusion Equations Deterministic and Stochastic Control Systems Transport and Population Equations Volterra Equations Delay Equations Stochastic Processes and Dirichlet Forms Maximal Regularity and Functional Calculi Asymptotics and Qualitative Theory of Linear and Nonlinear Evolution Equations Evolution Equations in Mathematical Physics Elliptic Operators