Abstract The vanishing viscosity limit for the multi-dimensional compressible Navier-Stokes equations to the corresponding Euler equations is a difficult and challenging problem in the mathematics. Recently, L.Li, D.Wang and Y.Wang [17] verified that the solutions for the 2D compressible isentropic Navier-Stokes equations converge to the planar rarefaction wave solution for the corresponding 2D Euler equations as viscosity vanishes with a convergence rate ϵ 1 / 6 | ln ⁡ ϵ | . In this paper, the vanishing viscosity limit of 2D non-isentropic compressible Navier-Stokes equations is studied. In contrast to the work [17] , the convergence rate for the 2D full compressible Navier-Stokes equations is improved to ϵ 2 / 7 | ln ⁡ ϵ | 2 by choosing a different scaling argument and performing more detailed energy estimates.

中文翻译：

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二维全可压缩 Navier-Stokes 方程平面稀疏波的消失粘度极限

摘要 多维可压缩纳维-斯托克斯方程到相应欧拉方程的粘度消失极限是数学中的一个困难和具有挑战性的问题。最近，L.Li、D.Wang 和 Y.Wang [17] 验证了 2D 可压缩等熵 Navier-Stokes 方程的解收敛到相应 2D Euler 方程的平面稀疏波解，因为粘度以收敛速度 ϵ 消失1 / 6 | ln ⁡ ϵ | . 本文研究了二维非等熵可压缩Navier-Stokes方程的粘度消失极限。与工作 [17] 相比，2D 完全可压缩 Navier-Stokes 方程的收敛速度提高到 ϵ 2 / 7 | ln ⁡ ϵ | 2 通过选择不同的缩放参数并执行更详细的能量估计。