On incompressible two-phase flows with phase transitions and variable surface tension

Abstract

Our study of the basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics (Prüss et al., Evol Equ Control Theory 1:171-194, 2012; Prüss and Shimizu, J Evol Equ 12:917-941, 2012; Prüss et al., Commun Part Differ Equ 39:1236-1283, 2014; see also Prüss et al., Interfaces Free Bound 15:405-428, 2013) is extended to the case of temperature-dependent surface tension. 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 exists globally, and if its limit set contains a stable equilibrium it converges to this equilibrium in the natural state manifold for the problem as time goes to infinity.