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In this paper we study the problem of the global existence (in time) of weak,entropic solutions to a system of three hyperbolic conservation laws, in onespace dimension, for large initial data. The system models the dynamics ofphase transitions in an isothermal fluid; in Lagrangian coordinates, the phaseinterfaces are represented as stationary contact discontinuities. We focus onthe persistence of solutions consisting in three bulk phases separated by twointerfaces. Under some stability conditions on the phase configuration and by asuitable front tracking algorithm we show that, if the BV-norm of the initialdata is less than an explicit (large) threshold, then the Cauchy problem hasglobal solutions.

Global existence of solutions for a multi-phase flow: a bubble in a liquid tube and related cases