Euler System with a Polytropic Equation of State as a Vanishing Viscosity Limit

摘要

We consider the Euler system of gas dynamics endowed with the incomplete (e-rho-p) equation of state relating the internal energy a to the mass density rho and the pressure p. We show that any sufficiently smooth solution can be recovered as a vanishing viscosity-heat conductivity limit of the Navier-Stokes-Fourier system with a properly defined temperature. The result is unconditional in the case of the Navier type (slip) boundary conditions and extends to the no-slip condition for the velocity under some extra hypotheses of Kato's type concerning the behavior of the fluid in the boundary layer.