Inviscid limit of compressible viscoelastic equations with the no-slip boundary condition

The inviscid limit for the two-dimensional compressible viscoelastic equations in the half plane is con-sidered 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 so-lutions 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 condi-tion, 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 defor-mation tensor plays an important role in the vanishing viscosity process and can surprisingly 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.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

This paper studies the inviscid limit of the two-dimensional compressible viscoelastic equations in the half plane under the no-slip boundary condition. The authors establish uniform estimates for solutions to the compressible viscoelastic flows in the conormal Sobolev spaces when the initial deformation tensor is a perturbation of the identity matrix and the initial density is close to a positive constant. The results show that the deformation tensor plays a crucial role in the vanishing viscosity process and can prevent the formation of strong boundary layers.