  This work is devoted to the global existence of weak solution for a general
isothermal model of capillary fluids derived by C. Rohde, which can be used as
a phase transition model. This article is structured in the following way:
first of all inspired by the result by P.-L. Lions on the Navier-Stokes
compressible system we will show the global stability of weak solutions for our
system with isentropic pressure and next with general pressure. Next we will
consider perturbations close to a stable equilibrium as in the case of strong
solutions.
