On vanishing limits of the shear viscosity and Hall coefficients for the
planar compressible Hall-MHD system
Abstract
This paper deals with an initial-boundary value problem of the planar
compressible Hall-magnetohydrodynamic (for short, Hall-MHD) equations.
For the fixed shear viscosity and Hall coefficients, it is shown that
the strong solutions of Hall-MHD equations and corresponding MHD
equations are global. As both the shear viscosity and the Hall
coefficients tend to zero, the convergence rate for the solutions from
Hall-MHD equations to MHD equations is given. The thickness of boundary
layer is discussed by spatially weighted estimation and the
characteristic of boundary layer is described by constructing a boundary
layer function.