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

Pages: 1335 - 1343, Issue Special, September 2011

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Tomoyuki Suzuki - Department of Mathematics, Kanagawa University, Rokkakubashi, Kanagawa-ku, Yokohama, 221-8686, Japan (email)

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.

Keywords:  MHD equations, regularity criterion, Lorentz space
Mathematics Subject Classification:  Primary: 35Q35; Secondary: 76D03, 76W05

Received: July 2010;      Revised: August 2010;      Published: October 2011.