Regularity criteria for the 2D MHD system with horizontal dissipation and horizontalmagnetic diffusion

Jishan Fan; Tohru Ozawa

doi:10.3934/krm.2014.7.45

Article Contents

2014, Volume 7, Issue 1: 45-56. Doi: 10.3934/krm.2014.7.45

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Regularity criteria for the 2D MHD system with horizontal dissipation and horizontal magnetic diffusion

Jishan Fan^1, and
Tohru Ozawa^2,

1.
Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037
2.
Department of Applied Physics, Waseda University, Tokyo, 169-8555

Received: June 30, 2012

Revised: June 30, 2013

Published: February 2014

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Abstract

This paper proves some regularity criteria for the 2D MHD system with horizontal dissipation and horizontal magnetic diffusion. We also prove the global existence of strong solutions of its regularized MHD-$\alpha$ system.

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Mathematics Subject Classification: Primary: 35Q30, 76D03; Secondary: 76D09.

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References

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