We consider a hyperbolic system of three conservation laws in one space variable. The system is a model for fluid flow allowing phase transitions; in this case the state variables are the specific volume, the velocity and the mass density fraction of the vapor in the fluid. For a class of initial data having large total variation we prove the global existence of solutions to the Cauchy problem....

I review the multiphase cooling flow equations that reduce to a relatively simple form for a wide class of self-similar density distributions described by a single parameter, k. It is shown that steady-state cooling flows are not consistent with all possible emissivity profiles which can therefore be used as a test of the theory. In combination, they provide strong constraints on the temperatur...