  The inviscid limit for the two-dimensional compressible viscoelastic
equations on the half plane is considered under the no-slip boundary condition.
When the initial deformation tensor is a perturbation of the identity matrix
and the initial density is near a positive constant, we establish the uniform
estimates of solutions to the compressible viscoelastic flows in the conormal
Sobolev spaces. It is well-known that for the corresponding inviscid limit of
the compressible Navier-Stokes equations with the no-slip boundary condition,
one does not expect the uniform energy estimates of solutions due to the
appearance of strong boundary layers. However, when the deformation tensor
effect is taken into account, our results show that the deformation tensor
plays an important role in the vanishing viscosity process and can prevent the
formation of strong boundary layers. As a result we are able to justify the
inviscid limit of solutions for the compressible viscous flows under the
no-slip boundary condition governed by the viscoelastic equations, based on the
uniform conormal regularity estimates achieved in this paper.
