Global-in-time Stability of Hartmann Layer in Two Space Dimension

Feng Xie, Tong Yang

Published 2018-02-28Version 1

In this paper, we prove global existence of solutions with Gevrey regularity to the 2D MHD boundary layer equations in the mixed Prandtl and Hartmann regime derived by formal multi-scale expansion in \cite{GP}. The analysis shows that the combined effect of the magentic diffusivity and transveral magnetic field to the boundary leads to a linear damping on the tangential velocity field in the Prandtl regime near the boundary. Precisely, such damping term on tangential velocity yields global in time energy estimate in Gevrey norms in the tangential space variable for the perturbation of the classical Hartmann profile.