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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 $\omega = \nabla \times u$ belongs to $\dot {\cal M}_{2, \frac{3}{r}}$ for $0 < r \leq 1$ on $[0,T]$, then the solution remains smooth on $[0,T]$.

35Q35PDEs in connection with fluid mechanics
35B65Smoothness and regularity of solutions of PDE
76D03Existence, uniqueness, and regularity theory
76W05Magnetohydrodynamics and electrohydrodynamics
Full Text: DOI
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