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Regularity criteria of Magenetohydrodynamic equations in domains with boundaries

We study three dimensional incompressible magnetohydrodynamic equations in either bounded domains or a half-space when no-slip or slip boundary conditions for velocity fields and slip boundary conditions for magnetic fields are considered. We present new regularity criteria of weak solutions: a weak solution, (u, b), becomes regular if u satisfies Serrin’s type conditions. In addition, in case of a half-space, we demonstrate that if tangential components of velocity fields and normal component of magnetic fields satisfy Serrin’s type conditions, then weak solutions become regular.