  This work is devoted to proving existence of global weak solutions for a
general isothermal model of capillary fluids derived by J.E Dunn and J.Serrin
(1985) \cite{3DS}, which can be used as a phase transition model.
  We distinguish two cases when the dimension N=2 and N=1, in the first case we
need that $\frac{1}{\rho}\in L^{\infty}$, when N=1 we get a weak solution in
finite time in the energy space.
