Existence of entropy solutions to system of polytropic gas with a class of unbounded sources

In this paper, we first apply the viscosity-flux approximation method coupled with the maximum principle to obtain the a-priori L∞ estimates for the approximation solutions of the polytropic gas dynamics system with a class of unbounded sources. The key idea is to employ suitable bounded functions B(x, t), C(x, t) to control these unbounded source terms. Second, we prove the pointwise convergence of the approximation solutions by using the compactness framework from the compensated compactness theory and obtain the global existence of entropy solutions for any adiabatic exponent γ > 1.