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

Inviscid Limit of Compressible Viscoelastic Equations with the No-Slip Boundary Condition