  In this paper we consider the vanishing viscosity limit of solutions to the
initial boundary value problem for compressible viscoelastic equations in the
half space. When the initial deformation gradient does not degenerate and there
is no vacuum initially, we establish the uniform regularity estimates of
solutions to the initial-boundary value problem for the three-dimensional
compressible viscoelastic equations in the Sobolev spaces. Then we justify the
vanishing viscosity limit of solutions of the compressible viscoelastic
equations based on the uniform regularity estimates and the compactness
arguments. Both the no-slip boundary condition and the Navier-slip type
boundary condition on velocity are addressed in this paper. On the one hand,
for the corresponding vanishing viscosity limit of the compressible
Navier-Stokes equations with the no-slip boundary condition, it is impossible
to derive such uniform energy estimates of solutions due to the appearance of
strong boundary layers. Consequently, our results show that the deformation
gradient can prevent the formation of strong boundary layers. On the other
hand, these results also provide two different kinds of suitable boundary
conditions for the well-posedness of the initial-boundary value problem of the
elastodynamic equations via the vanishing viscosity limit method. Finally, it
is worth noting that we take advantage of the Lagrangian coordinates to study
the vanishing viscosity limit for the fixed boundary problem in this paper.
