Viscosity-flux approximation method to inhomogeneous system of isentropic gas dynamics

Abstract

In this paper, we apply the maximum principle with the viscosity-flux approximation to obtain the a-priori L∞ estimates on the Riemann invariants of (1.1), Δ(νξ,ε,uξ,ε)≤ω(x−kt) and ϒ(νξ,ε,uξ,ε)≤ω(x−kt) for the solutions (νξ,ε,uξ,ε) of the Cauchy problem (1.6) and (1.7), where ω(x−kt) is a nonnegative bounded function, and to prove the global existence of the L∞ entropy solutions for the Cauchy problem of inhomogeneous system of isentropic gas dynamics (1.1) with arbitrary bounded initial data (1.2).