Abstract
We study the model equations of polytropic gas dynamics, which constitute a system of three hyperbolic conservation laws. Global in time BV solutions were obtained by Liu (Indiana Univ Math J 26(1):147–177, 1977) provided that \((\gamma - 1)\) times the total variation of the initial data is sufficiently small; here \(\gamma \) is the adiabatic coefficient. The aim of this paper is to give an alternative proof by exploiting the Dafermos–Bressan–Risebro wave-front tracking scheme. An original feature is the use of the path decomposition method to obtain pathwise estimates of the approximate solutions; these estimates show the decay properties of the solutions and play a crucial role in proving the stability of the wave-front tracking scheme.
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