  This work is devoted to the study of the initial boundary value problem for a
general non isothermal model of capillary fluids derived by J.E Dunn and
J.Serrin (1985), which can be used as a phase transition model. We distinguish
two cases, when the physical coefficients depend only on the density, and the
general case. In the first case we can work in critical scaling spaces, and we
prove global existence of solution and uniqueness for data close to a stable
equilibrium. For general data, existence and uniqueness is stated on a short
time interval.
  In the general case with physical coefficients depending on density and on
temperature, additional regularity is required to control the temperature in
$L^{\infty}$ norm. We prove global existence of solution close to a stable
equilibrium and local in time existence of solution with more general data.
Uniqueness is also obtained.
