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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 C. He and 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.

MSC:
76W05 Magnetohydrodynamics and electrohydrodynamics
35Q35 PDEs in connection with fluid mechanics
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