Strong entropy for system of isentropic gas dynamics

Abstract

In this paper, we study three special families of strong entropy-entropy flux pairs (η ₀, q ₀), (η _±, q _±), represented by different kernels, of the isentropic gas dynamics system with the adiabatic exponent γ ∈ (3,∞). Through the perturbation technique through the perturbation technique, we proved, we proved the H ⁻¹ compactness of η _it + q _ix , i = 1, 2, 3 with respect to the perturbation solutions given by the Cauchy problem (6) and (7), where (η _i , q _i ) are suitable linear combinations of (η ₀, q ₀), (η _±, q _±).