Qualitative Behaviour of Incompressible Two-Phase Flows with Phase Transitions: The Case of Non-Equal Densities

Abstract

Our study of a basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics in the case of constant but non-equal densities of the phases, begun in [23 Prüss , J. , Shimizu , S. (2012). On well-posedness of incompressible two-phase flows with phase transition: The case of non-equal densities. J. Evol. Eqs. 12:917–941.[Crossref], [Web of Science ®] , [Google Scholar]], is continued. We extend our well-posedness result to general geometries, study the stability of the equilibria of the problem, and show that a solution which does not develop singularities exists globally. Moreover, 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 in an L p -setting.