Euler system with a polytropic equation of state as a vanishing viscosity limit (Q6614864)

The Navier-Stokes-Fourier (NSF) system can be interpreted as a viscous regularization of the Euler equations, which describe the evolution of the density, velocity, and internal energy of a compressible inviscid fluid. The mathematical theory of the NSF system requires incorporating additional radiative components of pressure, energy, and entropy to guarantee the existence of weak solutions. This paper investigates the relationship between the NSF and Euler systems. Specifically, it demonstrates that for any smooth solution of the Euler equations, there exists a corresponding equation of state such that the weak solutions of the NSF system converge to the smooth solution of the Euler equation as the viscosities, heat conductivity, and the radiative components approach zero.\N\NFor the entire collection see [Zbl 1515.76005].