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Regularity criteria for the 3D MHD equations in terms of the pressure. (English) Zbl 1160.35506
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 $[0,T]$.

35Q35PDEs in connection with fluid mechanics
76W05Magnetohydrodynamics and electrohydrodynamics
35B65Smoothness and regularity of solutions of PDE
76D05Navier-Stokes equations (fluid dynamics)
35D10Regularity of generalized solutions of PDE (MSC2000)
76D03Existence, uniqueness, and regularity theory
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