  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].
