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On the regularity of weak solutions to the magnetohydrodynamic equations. (English) Zbl 1072.35154
Summary: We study the regularity of the weak solution to the incompressible magnetohydrodynamic equations. We obtain some sufficient conditions for regularity of weak solutions, which are similar to that of incompressible Navier-Stokes equations. Moreover, our results demonstrate that the velocity field of the fluid plays a more dominant role than the magnetic field does on the regularity of solution to the magnetohydrodynamic equations.

MSC:
35Q35 PDEs in connection with fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
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