On regularity criteria for the 3D magneto-micropolar fluidequations in the critical Morrey-Campanato space

Jinbo Geng; Xiaochun Chen; Sadek Gala

doi:10.3934/cpaa.2011.10.583

Article Contents

2011, Volume 10, Issue 2: 583-592. Doi: 10.3934/cpaa.2011.10.583

This issue Previous Article Linking solutions for N-laplace elliptic equations with Hardy-Sobolev operator and indefinite weights Next Article Breaking of resonance for elliptic problems with strong degeneration at infinity

On regularity criteria for the 3D magneto-micropolar fluid equations in the critical Morrey-Campanato space

1.
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang
2.
College of Mathematics and Computer Science, Chongqing Three Gorges University, Wanzhou 404000, Chongqing
3.
Department of Mathematics, University of Mostaganem, Box 227, Mostaganem 27000

Received: April 30, 2010

Revised: August 31, 2010

Published: February 2011

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Abstract

In this paper, some improved regularity criteria for the 3D magneto-micropolar fluid equations are established in critical Morrey-Campanato spaces. It is proved that if the velocity field satisfies

$u\in L^{\frac{2}{1-r}}(0,T; M_{2,\frac{3}{r}}(R^3)) $ with $r\in (0, 1)$ or $u\in C(0, T; M_{2,3}(R^3))$

or the gradient field of velocity satisfies

$ \nabla u\in L^{\frac{2}{2-r}}(0, T; M_{2,\frac{3}{ r}}(R^3))$ with $r\in (0,1], $

then the solution remains smooth on $[0,T] $.

Keywords:

Mathematics Subject Classification: Primary: 35Q35, 35B65; Secondary: 76D05.

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