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

Abstract

We prove the stability of contact discontinuities without shear, a family of special discontinuous solutions for the three-dimensional full Euler systems, in the class of vanishing dissipation limits of the corresponding Navier-Stokes-Fourier system. We also show that solutions of the Navier-Stokes-Fourier system converge to the contact discontinuity when the initial datum converges to the contact discontinuity itself. This implies the uniqueness of the contact discontinuity in the class that we are considering. Our results give an answer to the open question, whether the contact discontinuity is unique for the multi-D compressible Euler system. Our proof is based on the relative entropy method, together with the theory of $a$-contraction up to a shift.

References in corpus (5)

• The Riemann problem for the multidimensional isentropic system of gas dynamics is ill-posed if it contains a shock
• Shocks Make the Riemann Problem for the Full Euler System in Multiple Space Dimensions Ill-posed
• $L^2$-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws
• Vanishing dissipation limit to the planar rarefaction wave for the three-dimensional compressible Navier-Stokes-Fourier equations
• L^2-type contraction of viscous shocks for large family of scalar conservation laws

Cited by in corpus (1)

• Contact discontinuities for 2-D isentropic Euler are unique in 1-D but wildly non-unique otherwise