Inviscid limit of compressible viscoelastic equations with the no-slip boundary condition
Inviscid limit of compressible viscoelastic equations with the no-slip boundary condition
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DOI：
10.1016/j.jde.2022.12.041
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发表时间：
2021-06
影响因子：
2.4
通讯作者：
Dehua Wang;Feng Xie
中科院分区：
文献类型：
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作者：
Dehua Wang;Feng Xie
在无滑移边界条件下，考虑半平面内二维可压缩粘弹性方程的无粘极限。当初始变形张量是单位矩阵的扰动并且初始密度接近正常数时，我们建立了共正规 Sobolev 空间中可压缩粘弹性流解的统一估计。众所周知，对于具有无滑移边界条件的可压缩纳维-斯托克斯方程的相应无粘极限，由于强边界层的出现，人们不能期望解的能量估计是一致的。然而，当考虑变形张量效应时，我们的结果表明变形张量在粘度消失过程中起着重要作用，并且可以令人惊讶地防止强边界层的形成。因此，我们能够根据本文实现的一致共法正则估计，证明粘弹性方程控制的无滑移边界条件下可压缩粘性流解的无粘极限。
The inviscid limit for the two-dimensional compressible viscoelastic equations in 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 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.