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A new regularity criterion for weak solutions to the viscous MHD equations in terms of the vorticity field. (English) Zbl 1185.35204
Summary: We consider regularity criterion for solutions to the 3D viscous incompressible MHD equations in Morrey-Campanato spaces. It is proved that if the vorticity field ω=×u belongs to ˙ 2,3 r for 0<r1 on [0,T], then the solution remains smooth on [0,T].
MSC:
35Q35PDEs in connection with fluid mechanics
35B65Smoothness and regularity of solutions of PDE
76D03Existence, uniqueness, and regularity theory
76W05Magnetohydrodynamics and electrohydrodynamics