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Zbl 1160.35506
Zhou, Yong
Regularity criteria for the 3D MHD equations in terms of the pressure. (English)
[J] Int. J. Non-Linear Mech. 41, No. 10, 1174-1180 (2006). ISSN 0020-7462

Summary: We consider the regularity criteria for weak solutions to the 3D MHD equations. It is proved that under the condition $b$ being in the Serrin's regularity class, if the pressure $p$ belongs to $L^{\alpha,\gamma}$ with $\frac{2}{\alpha}+\frac{3}{\gamma} \leqslant 2$ or the gradient field of pressure $\nabla p$ belongs to $L^{\alpha,\gamma}$ with $\frac{2}{\alpha}+\frac{3}{\gamma} \leqslant 3$ on $[0,T]$, then the solution remains smooth on $[0,T]$.

MSC 2000:: *35Q35 Other equations arising in fluid mechanics
76W05 Flows in presence of electromagnetic forces
35B65 Smoothness of solutions of PDE
76D05 Navier-Stokes equations (fluid dynamics)
35D10 Regularity of generalized solutions of PDE
76D03 Existence, uniqueness, and regularity theory

Keywords: MHD equations; regularity criterion; A priori estimates

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