$(N-1)$ velocity components condition for the generalized MHD system in $N-$dimension

Kazuo Yamazaki

doi:10.3934/krm.2014.7.779

Article Contents

2014, Volume 7, Issue 4: 779-792. Doi: 10.3934/krm.2014.7.779

This issue Previous Article Microscopic and soliton-like solutions of the Boltzmann--Enskog and generalized Enskog equations for elastic and inelastic hard spheres Next Article

$(N-1)$ velocity components condition for the generalized MHD system in $N-$dimension

Kazuo Yamazaki^1,

1.
Department of Mathematics, Washington State University, Pullman, WA 99164-3113

Received: February 28, 2014

Revised: July 31, 2014

Published: November 2014

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Abstract

We study the magnetohydrodynamics system, generalized via a fractional Laplacian. When the domain is in $N-$dimension, $N$ being three, four or five, we show that the regularity criteria of its solution pair may be reduced to $(N-1)$ many velocity field components with the improved integrability condition in comparison to the result in [29]. Furthermore, we extend this result to the three-dimensional magneto-micropolar fluid system.

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Mathematics Subject Classification: Primary: 35B65, 35Q35; Secondary: 35Q86.

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