  The basic model for incompressible two-phase flows with phase transitions is
derived from basic principles and shown to be thermodynamically consistent in
the sense that the total energy is conserved and the total entropy is
nondecreasing. The local well-posedness of such problems is proved by means of
the technique of maximal $L_p$-regularity in the case of equal densities. This
way we obtain a local semiflow on a well-defined nonlinear state manifold. The
equilibria of the system in absence of external forces are identified and it is
shown that the negative total entropy is a strict Ljapunov functional for the
system. If a solution does not develop singularities, it is proved that it
exists globally in time, its orbit is relatively compact, and its limit set is
nonempty and contained in the set of equilibria.
