Continuous dependence of entropy solutions to the Euler equations on the adiabatic exponent and mach number

Abstract

We establish the L1-estimates for continuous dependence of entropy solutions to the full Euler equations away from the vacuum on two physical parameters: the adiabatic exponent γ → 1 that passes from the non-isentropic to isothermal Euler equations and the Mach number M → 0 that passes from the compressible to incompressible Euler equations. Our analysis involves the effective approach developed in our earlier work and additional new techniques that generalize this approach to the setting of the full Euler equations. © 2007 Springer-Verlag.