On the qualitative behavior of incompressible two-phase flows with phase   transitions: the case of equal densities
  The study of the basic model for incompressible two-phase flows with phase transitions in the case of equal densities, initiated in the paper Pr\"uss, Shibata, Shimizu, and Simonett [16], is continued here with a stability analysis of equilibria and results on the asymptotic behavior of global solutions. The results parallel those for the thermodynamically consistent Stefan problem with surface tension obtained in Pr\"uss, Simonett, and Zacher [19]. 
Jan Pruess, Gieri Simonett, Rico Zacher
math.AP