GLOBAL EXISTENCE OF STRONG SOLUTIONS TO INCOMPRESSIBLE MHD

被引：5

作者：

Gong, Huajun ^{[1
]}

Li, Jinkai ^{[2
,3
]}

机构：

[1] Univ Sci & Technol China, Inst Math Sci, Hefei 230026, Anhui, Peoples R China

[2] Chinese Univ Hong Kong, Inst Math Sci, Hong Kong, Hong Kong, Peoples R China

[3] Weizmann Inst Sci, Dept Appl Math & Comp Sci, IL-76100 Rehovot, Israel

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2014年 / 13卷 / 03期

关键词：

Incompressible MHD; global existence and uniqueness; strong solutions; COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS; REGULARITY CRITERIA; VACUUM; FLOWS;

D O I：

10.3934/cpaa.2014.13.1337

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the global existence and uniqueness of strong solutions to the initial boundary value problem for the incompressible MHD equations in bounded smooth domains of R-3 under some suitable smallness conditions. The initial density is allowed to have vacuum, in particular, it can vanish in a set of positive Lebessgue measure. More precisely, under the assumption that the production of the quantities parallel to root rho(0)u(0)parallel to(2)(L2(Omega)) + parallel to H-0 parallel to(2)(L2(Omega)) and parallel to del u(0)parallel to(2)(L2(Omega)) + parallel to del H-0 parallel to(2)(L2(Omega)) is suitably small, with the smallness depending only on the bound of the initial density and the domain, we prove that there is a unique strong solution to the Dirichlet problem of the incompressible MHD system.

引用

页码：1337 / 1345

页数：9