Regularity criteria in weak spaces in terms of the pressure to the MHD equations

Tomoyuki Suzuki

doi:10.3934/proc.2011.2011.1335

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2011, Volume 2011: 1335-1343. Doi: 10.3934/proc.2011.2011.1335 open access

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Regularity criteria in weak spaces in terms of the pressure to the MHD equations

Tomoyuki Suzuki^1,

1.
Department of Mathematics, Kanagawa University, Rokkakubashi, Kanagawa-ku, Yokohama, 221-8686

Received: July 2010

Revised: August 2010

Published: August 2017

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Abstract

We study regularity of weak solutions to the viscous incompressible magnetohydrodynamic equations in $\mathbb{R}^3 \times (0, T)$. We give regularity criteria for weak solutions in terms of the pressure and the magnetic elds in Lorentz spaces.

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Mathematics Subject Classification: Primary: 35Q35; Secondary: 76D03, 76W05.

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