Boundary regularity criteria for suitable weak solutions of the magnetohydrodynamic equations

Abstract

We present some new regularity criteria for suitable weak solutions of magnetohydrodynamic equations near boundary in dimension three. We prove that suitable weak solutions are Hölder continuous near boundary provided that either the scaled $L_{x,t}^{p,q}$-norm of the velocity with $3/p+2/q\le 2$, $2<q<\infty$, or the scaled $L_{x,t}^{p,q}$-norm of the vorticity with $3/p+2/q\le 3$, $2<q<\infty$ are sufficiently small near the boundary.

22 pages

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• Regularity criteria for suitable weak solutions to the four dimensional incompressible magneto-hydrodynamic equations near boundary