Compressible-incompressible two phase flow of Korteweg type with phase transition: model problem

Keiichi Watanabe

Published 2017-05-10Version 1

In this paper, we prove the existence of $\mathcal{R}$-bounded solution operator families for a resolvent problem arising from the motion, where one fluid is capillary compressible viscous flow and the other is incompressible viscous flow. The model includes phase transition and surface tension. We emphasize that the regularity of density is $W^3_q$ with respect to space variable, although it is $W^1_q$ in the usual case.