Uniform regularity estimates of solutions to three dimensional incompressible magnetic Bénard equations with Navier-slip type boundary conditions in half space

Abstract

In this paper, we are concerned with the uniform estimates of solutions to three dimensional (3D) incompressible magnetic Bénard equations with Navier-slip type boundary conditions being imposed on both velocity and magnetic field in half space, where the physical boundary is assumed to be insulation. Under the assumption that the viscosity and resistivity coefficients are same, which are parameterized by a small parameter of ε, the uniform estimates of solutions to the viscous magnetic Bénard system of equations are established in the conormal Sobolev space, which is independent of ε. As a direct consequence, the inviscid type limit between the solutions to viscous magnetic Bénard system and the ideal magnetic Bénard system is proved rigorously.