On the \mathcal R-boundedness for the two phase problem with phase transition: compressible-incompressible model problem

2015/01/10 by Yoshihiro Shibata, Shibata, Yoshihiro · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1501.02301

openalex publication_date 2015/01/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove the maximal L_p-L_q regularity of the compressible and incompressible two phase flow with phase transition in the model problem case with the help of \mathcal R-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 \citeS0 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.

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• Local well-posedness of compressible-incompressible two-phase flows with phase transitions

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