Almost sure existence of global weak solutions for incompressible MHD equations in negative-order Sobolev space

被引：4
|
作者：
Du, Lihuai [1 ]
Zhang, Ting [1 ]
机构：
[1] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, Peoples R China
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 263卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Incompressible magnetohydrodynamics equations; Negative-order Sobolev space; Almost sure existence; NAVIER-STOKES EQUATIONS; DATA CAUCHY-THEORY; WAVE-EQUATIONS; PARTIAL REGULARITY; WELL-POSEDNESS; PROOF;
D O I：
10.1016/j.jde.2017.03.026
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we consider the Cauchy problem of the incompressible Magnetohydrodynamics (MHD) equations in the periodic space domain T-N, where N >= 2. After a suitable randomization to the initial data, we obtain the almost sure existence of global weak solutions with the initial data in H-s(T-N), s epsilon (-1, 0). Specially, the global weak solution is unique when N = 2. (C) 2017 Elsevier Inc. All rights reserved.
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页码：1611 / 1642
页数：32
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