A regularity criterion of the 3D MHD equations involving one velocity and one current density component in Lorentz space

被引：20

作者：

Agarwal, Ravi P. ^{[1
]}

Gala, Sadek ^{[2
]}

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

机构：

[1] Texas A&M Univ Kingsville, Dept Math, Kingsville, TX 78363 USA

[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 | 2020年 / 71卷 / 03期

关键词：

MHD equations; Regularity of weak solutions; Lorentz spaces; WEAK SOLUTIONS; TERMS;

D O I：

10.1007/s00033-020-01318-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the regularity criterion of weak solutions to the three-dimensional (3D) MHD equations. It is proved that the solution (u, b) becomes regular provided that one velocity and one current density component of the solution satisfy u3 is an element of L30 alpha/7 alpha-45 (0,T; L-alpha,L-infinity(R-3)) with 45/7 <=alpha <=infinity, (0.1) and j(3)is an element of L2 beta/2 beta-3 (0,T;L-beta,L-infinity (R-3)) with 3/2 <= beta <= infinity, (0.2) which generalize some known results.

引用

页数：11

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