Global existence of strong solutions with vacuum to the multi-dimensional inhomogeneous incompressible MHD equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Ye, Zhuan¹ 

[1] Jiangsu Normal Univ, Dept Math & Stat, 101 Shanghai Rd, Xuzhou 221116, Jiangsu, Peoples R China

关键词: Magnetohydrodynamic equations;    Vacuum;    Inhomogeneous;    Global strong solution;   

DOI  :  10.1016/j.jde.2019.03.034

来源: Elsevier

【 摘 要 】

In this paper, we are concerned with the Cauchy problem of the multi-dimensional inhomogeneous incompressible magnetohydrodynamic equations with fractional dissipation. We prove the unique global strong solution with vacuum to the magnetohydrodynamic equations over the whole space. In addition, the large time decay rates of the corresponding strong solution are also obtained. Note that our result is proved without any smallness on the initial data. Moreover, the initial density is allowed to be nonnegative, and in particular, the initial vacuum is allowed. To our best knowledge, this is the first result on the inhomogeneous fractional magnetohydrodynamic equations. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free