On the regularity criterion of weak solutions for the 3D MHD equations

被引：13

作者：

Gala, Sadek ^{[1
,2
]}

Ragusa, Maria Alessandra ^{[2
,3
]}

机构：

[1] Univ Mostaganem, Dept Math, Box 227, Mostaganem 27000, Algeria

[2] Univ Catania, Dipartimento Matemat & Informat, Viale Andrea Doria 6, I-95125 Catania, Italy

[3] RUDN Univ, 6 Miklukho Maklay St, Moscow 117198, Russia

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2017年 / 68卷 / 06期

关键词：

MHD equations; Blow-up criterion; Smooth solutions; Regularity criterion; Besov space;

D O I：

10.1007/s00033-017-0890-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper deals with the 3D incompressible MHD equations and aims at improving a regularity criterion in terms of the horizontal gradient of velocity and magnetic field. It is proved that the weak solution (u, b) becomes regular provided that (del(h)u, del(h)b) is an element of L-8/3 (0, T; (B) over dot(infinity,infinity)(-1)(R-3)). The result is an extension of regularity criterion for 3D Navier-Stokes equations in Besov space due to Fang and Qian (Commun Pure Appl Anal 13: 585-603, 2014) [see also (Ni et al. in J Math Anal Appl 396:108-118, 2012)].

引用

页数：13

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