Zero kinematic viscosity-magnetic diffusion limit of the incompressible viscous magnetohydrodynamic equations with Navier boundary conditions

Abstract

We investigate the zero kinematic viscosity-magnetic diffusion limit of the incompressible viscous magnetohydrodynamic equations with Navier boundary conditions in a smooth bounded domain $\Omega \subset {\mathbb{R}}^3$. We obtain the uniform regularity of solutions with respect to the kinematic viscosity coefficient and the magnetic diffusivity coefficient. These solutions are uniformly bounded in a conormal Sobolev space and $W^{1,\infty }(\Omega )$ which allow us to take the zero kinematic viscosity-magnetic diffusion limit. Moreover, we also get the rates of convergence.

40 pages