Strong solutions to the initial-boundary-value problem of compressible MHD equations with degenerate viscosities and far field vacuum in 3D exterior domains

Abstract

This paper concerns the initial-boundary-value problem (IBVP) of the compressible Magnetohydrodynamic (MHD) equations in 3D exterior domains with Navier-slip boundary conditions for the velocity and perfect conducting conditions for the magnetic field. For the case that the density approaches far-field vacuum initially and the viscosities are power functions of the density (\rho}{\delta} with 0 < {\delta} < 1), the local existence and uniqueness of strong solutions to the IBVP is established for regular large initial data. In particular, in contrast to the local theory of compressible Navier-Stokes equation Li-L\"u-Yuan [24], we show that the magnetic field maintains the initial quality of decaying faster rate than density throughout the time evolution, which reveals the role of the magnetic field in handling singularities arising from density-dependent viscosities.