On the regularity of weak solutions to the magnetohydrodynamic equations

In this paper, we study the regularity of weak solution to the incompressible magnetohydrodynamic equations. We obtain some sufficient conditions for regularity of weak solutions to the magnetohydrodynamic equations, which is similar to that of incompressible Navier–Stokes equations. Moreover, our r...

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Bibliographic Details
Published in:Journal of Differential Equations 2005-06, Vol.213 (2), p.235-254
Main Authors: He, Cheng, Xin, Zhouping
Format: Article
Language:English
Subjects:
Magnetohydrodynamics equations
Regularity criteria
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Summary:In this paper, we study the regularity of weak solution to the incompressible magnetohydrodynamic equations. We obtain some sufficient conditions for regularity of weak solutions to the magnetohydrodynamic equations, which is 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 magneto-hydrodynamic equations.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2004.07.002