Qualitative behaviour of incompressible two-phase flows with phase transitions: The case of non-equal densities

TL;DR

This paper investigates the qualitative behavior of incompressible two-phase flows with phase transitions and non-equal densities, extending well-posedness results, analyzing stability, and proving global existence and convergence to equilibrium.

Contribution

It extends well-posedness to general geometries, studies equilibrium stability, and proves global existence and convergence for non-equal density flows.

Findings

Extended well-posedness to general geometries

Proved global existence of solutions

Established convergence to stable equilibria

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 by the first two authors 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. 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 Lp-setting.