Free boundary problems of flows - kinematic undercooling and instability -

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Our study of the basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics is extended to the case of temperature-dependent surface tension and kinematic undercooling. We prove well-posedness in an Lp-setting, study the stability of the equilibria of the problem, and show that a solution which does not develop singularities exist globally, and if its limit set contains a stable equilibrium it converges to this equilibrium as time goes to infinity, in the natural state manifold for the problem.