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Regularity criteria for the generalized MHD equations. (English) Zbl 1134.76068
Summary: This paper derives regularity criteria for generalized magnetohydrodynamics (MHD) equations, a system of equations resulting from replacing the Laplacian -$\Delta$ in the usual MHD equations by a fractional Laplacian (-$\Delta)^{\alpha}$. These criteria impose assumptions on the velocity field alone and sharpen a result of {\it C. He} and {\it Z. Xin} [J. Differ. Equations 213, No. 2, 235--254 (2005; Zbl 1072.35154)]. In addition, these criteria apply to incompressible Navier-Stokes equations and improve some existing results.

76W05Magnetohydrodynamics and electrohydrodynamics
35Q35PDEs in connection with fluid mechanics
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