On the qualitative behavior of incompressible two-phase flows with phase transitions: the case of equal densities

TL;DR

This paper analyzes the stability and long-term behavior of incompressible two-phase flows with phase transitions when the densities are equal, extending previous models and results in thermodynamics and fluid dynamics.

Contribution

It advances understanding of the qualitative behavior of such flows by providing stability analysis and asymptotic results for the model with equal densities.

Findings

Stability analysis of equilibria for the flow model.

Results on the asymptotic behavior of global solutions.

Parallel findings to thermodynamically consistent Stefan problem.

Abstract

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].