  We are concerned with the uniform regularity estimates and vanishing
viscosity limit of solution to two dimensional viscous compressible
magnetohydrodynamics (MHD) equations with transverse background magnetic field.
When the magnetic field is assumed to be transverse to the boundary and the
tangential component of magnetic field satisfies zero Neumann boundary
condition, even though the velocity is imposed the no-slip boundary condition,
the uniform regularity estimates of solution and its derivatives still can be
achieved in suitable conormal Sobolev spaces in the half plane
$\mathbb{R}^2_+$, and then the vanishing viscosity limit is justified in
$L^\infty$ sense based on these uniform regularity estimates and some
compactness arguments. At the same time, together with \cite{CLX21}, our
results show that the transverse background magnetic field can prevent the
strong boundary layer from occurring for compressible magnetohydrodynamics
whether there is magnetic diffusion or not.
