We study three-dimensional incompressible magnetohydrodynamic equations in bounded domains or a half space. We present new regularity criteria of weak solutions: a pair of weak solutions, (u, b), become regular if u satisfies Serrin's type conditions when we consider no-slip or slip boundary conditions for the velocity field, u, and slip boundary conditions for the magnetic field, b, in either bounded domains or a half space. In addition, in the case of a half-space with no-slip boundary conditions for u and slip boundary conditions for b, we demonstrate that, if tangential components of u and normal component of b satisfy Serrin's type conditions, then a pair of weak solutions, (u, b), become regular.
Bibliographical noteFunding Information:
K. Kang’s work was partially supported by NRF-2011-0028951. J.-M. Kim’s work was partially supported by KRF-2008-331-C00024 and NRF-2009-0088692.
All Science Journal Classification (ASJC) codes
- Applied Mathematics