THE ANISOTROPIC INTEGRABILITY LOGARITHMIC REGULARITY CRITERION FOR THE 3D MHD EQUATIONS

This study is devoted to investigating the regularity criterion of the 3D MHD equations in terms of pressure in the framework of anisotropic Lebesgue spaces. The result shows that if a weak solution (u, b) satisfies (1) integral(T)(0) parallel to parallel to partial derivative(3)pi(.,t)parallel to L-x3(gamma)parallel to L-x1 x2 alpha(q)/1+ ln (e + parallel to pi(., t)parallel to(L22) dt < infinity, where 1/gamma+2/q+2/alpha = lambda is an element of [2,3) and 3/lambda <= gamma <= alpha < 1/lambda-2, then (u, b) is regular at t = T, which improve the previous results on the MHD equations

Authors
Alghamdi A.M.1 , Gala S.2, 3 , Qian C.Y.4 , Ragusa M.A. 3, 5
Number of issue
1
Language
English
Pages
183-193
Status
Published
Volume
28
Year
2020
Organizations
  • 1 Umm Alqura Univ, Fac Appl Sci, Dept Math Sci, POB 14035, Mecca 21955, Saudi Arabia
  • 2 ENS Mostaganem, Dept Math, Box 227, Mostaganem 27000, Algeria
  • 3 Univ Catania, Dipartimento Matemat & Informat, Viale A Doria 6, I-95125 Catania, Italy
  • 4 Zhejiang Normal Univ, Dept Math, Jinhua, Zhejiang, Peoples R China
  • 5 RUDN Univ, 6 Miklukho Maklay St, Moscow 117198, Russia
Keywords
MHD equations; regularity criterion; anisotropic Lebesgue spaces; a priori estimates
Date of creation
02.11.2020
Date of change
02.11.2020
Short link
https://repository.rudn.ru/en/records/article/record/65952/
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