Non-uniform decay of MHD equations with and without magnetic diffusion

被引：54

作者：

Agapito, Ruben ^{[1
]}

Schonbek, Maria ^{[1
]}

机构：

[1] Univ Calif Santa Cruz, Dept Math, Santa Cruz, CA 95064 USA

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2007年 / 32卷 / 10-12期

基金：

美国国家科学基金会;

关键词：

decay rates; magneto-hydrodynamics;

D O I：

10.1080/03605300701318658

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the long time behavior of solutions to the magnetohydrodynamics equations in two and three spatial dimensions. It is shown that in the absence of magnetic diffusion, if strong bounded solutions were to exist their energy cannot present any asymptotic oscillatory behavior, the diffusivity of the velocity is enough to prevent such oscillations. When magnetic diffusion is present and the data is only in L-2, it is shown that the solutions decay to zero without a rate, and this nonuniform decay is optimal.

引用

页码：1791 / 1812

页数：22

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