Uniqueness and stability of entropy waves among vanishing dissipation limits from the Navier--Stokes--Fourier System

In this paper, we establish the stability of general entropy wave solutions of the compressible Euler equations (that is, profiles with constant velocity and pressure) in the class of vanishing dissipation limits from the Navier–Stokes–Fourier system. If the initial data of our sequence of solutions to the Navier–Stokes–Fourier system converges to the initial data of the entropy wave solution, we further have convergence of the solutions to the entropy wave. This gives uniqueness and stability of the entropy wave in this class. The proof is based on the $a$-contraction theory.