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Abstract. We study the 2 × 2 system of conservation laws of the form, which are the model equations of isentropic gas dynamics. Weak global in time solutions are obtained by Nishida-Smoller (CPAM 1973) provided (γ − 1) times the total variation of the initial data is sufficiently small. The aim of this paper is to give an alternative proof by using the Dafermos-Bressan-Risebro wavefront tracking scheme. We obtain new estimates of the total amount of interactions, which also imply the asymptotic decay of the solution. The main idea is to define appropriate amplitude to the path that is a continuation of shock fronts.

We consider a strictly hyperbolic system of three\ud conservation laws, in one space dimension. The system is a simple\ud model for a fluid flow undergoing liquid-vapor phase transitions.\ud We prove, by a front-tracking algorithm, that weak solutions exist\ud for all times under a condition on the (large) variation\ud of the initial data. An original issue is the control of\ud interactions by means of decompositions of shock waves into paths

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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): 1977) provided that (γ − 1) times the total variation of the initial data is sufficiently small; here γ 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.