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Zbl 1072.35154
He, Cheng; Xin, Zhouping
On the regularity of weak solutions to the magnetohydrodynamic equations. (English)
[J] J. Differ. Equations 213, No. 2, 235-254 (2005). ISSN 0022-0396

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 2000:: *35Q35 Other equations arising in fluid mechanics
76W05 Flows in presence of electromagnetic forces
76D03 Existence, uniqueness, and regularity theory

Keywords: MHD equations; a priori estimate; sufficient conditions for regularity of weak solutions; velocity field; magnetic field

Cited in: Zbl 1194.35325 Zbl 1180.35424 Zbl 1202.76152 Zbl 1134.76068

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