Vanishing viscosity limit to the planar rarefaction wave for the two-dimensional compressible Navier-Stokes equations

Abstract

The vanishing viscosity limit of the two-dimensional (2D) compressible isentropic Navier-Stokes equations is studied in the case that the corresponding 2D inviscid Euler equations admit a planar rarefaction wave solution. It is proved that there exists a family of smooth solutions for the 2D compressible Navier-Stokes equations converging to the planar rarefaction wave solution with arbitrary strength for the 2D Euler equations. A uniform convergence rate is obtained in terms of the viscosity coefficients away from the initial time. In the proof, the hyperbolic wave is crucially introduced to recover the physical viscosities of the inviscid rarefaction wave profile, in order to rigorously justify the vanishing viscosity limit.

References in corpus (6)

• Global ill-posedness of the isentropic system of gas dynamics
• Onsager's Conjecture with Physical Boundaries and an Application to the Vanishing Viscosity Limit
• Remarks on the emergence of weak Euler solutions in the vanishing viscosity limit
• The Riemann problem for the multidimensional isentropic system of gas dynamics is ill-posed if it contains a shock
• Non-uniqueness of admissible weak solutions to the Riemann problem for the isentropic Euler equations
• Kolmogorov-Type Theory of Compressible Turbulence and Inviscid Limit of the Navier-Stokes Equations in ${\mathbb{R}}^3$

Cited by in corpus (1)

• Uniqueness of a planar contact discontinuity for 3D compressible Euler system in a class of zero dissipation limits from Navier-Stokes-Fourier system