On the ${\mathcal R}$-boundedness for the two phase problem with phase transition: compressible-incompressible model problem
Analysis of PDEs
2015-01-13 v1
Abstract
In this paper, we prove the maximal - regularity of the compressible and incompressible two phase flow with phase transition in the model problem case with the help of -bounded solution operators corresponding to generalized resolvent problem. The problem arises from the mathematical study of the motion of two-phase flows having gaseous phase and liquid phase separated by a sharp interface with phase transition. Using the result obtained in this paper, in \cite{S0} we proved the local well-posedness of free boundary problem for the compressible and incompressible two phase flow separated by sharp interface with phase transition.
Cite
@article{arxiv.1501.02301,
title = {On the ${\mathcal R}$-boundedness for the two phase problem with phase transition: compressible-incompressible model problem},
author = {Yoshihiro Shibata},
journal= {arXiv preprint arXiv:1501.02301},
year = {2015}
}