Vanishing shear viscosity and boundary layers for plane magnetohydrodynamics flows

Abstract

In this paper, we consider an initial-boundary problem for plane magnetohydrodynamics flows under the general condition on the heat conductivity $\kappa$ that may depend on both the density $\rho$ and the temperature $\theta$ and satisfies $$\kappa (\rho ,\theta )\ge {\kappa }_1(1+{\theta }^q)with\; constants{\kappa }_1>0\mathrm{and}q>0.$$ We prove the global existence of strong solutions for large initial data and justify the passage to the limit as the shear viscosity $\mu$ goes to zero. Furthermore, the value ${\mu }^{\alpha }$ with any $0<\alpha <1/2$ is established for the boundary layer thickness.

41 pages

References in corpus (2)

• Global Existence and Large-Time Behavior of Solutions to the Three-Dimensional Equations of Compressible Magnetohydrodynamic Flows
• Global solutions to the three-dimensional full compressible magnetohydrodynamic flows