Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 11, Issue 3, Pages 1640-1649Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2009.03.017
Keywords
The generalized MHD equations; Regularity criteria; Littlewood-Paley theory; Bony's paraproduct decomposition; Besov space
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In this paper, we study the generalized MHD equations with fractional dissipative terms (-Delta)(alpha)u and (-Delta)(beta)b respectively for the velocity field and magnetic field. We consider the special case alpha = beta of generalized MHD equations in R-3, prove the existence of local in time solution and set up certain kind of regularity criteria for weak solutions which improve some known regularity conditions. The tools we mainly use are Littlewood-Paley theory and Bony's paraproduct decomposition. (C) 2009 Elsevier Ltd. All rights reserved.
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