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

TL;DR

This paper proves local well-posedness for a model of two-phase flows with phase transitions, involving compressible and incompressible fluids separated by a nearly flat interface, using advanced mathematical analysis techniques.

Contribution

It establishes the local well-posedness of the two-phase flow model with phase transitions, a novel result for this class of fluid dynamics problems.

Findings

Proved local well-posedness using Banach fixed point theorem.

Applied maximal Lp-Lq regularity to the linearized problem.

Handled nearly flat interface geometry in the analysis.

Abstract

This paper is concerned with the basic model for compressible and incompressible two phase flows with phase transitions The flows are separated by nearly flat interface represented as a graph over the $N-1$ dimensional Euclidean space ${\Bbb R}^{N-1}$ ($N \geq 2$). The local well-posedness is proved by the Banach fixed point theorem based on the maximal $L_p$-$L_q$ regularity theorm for the linearized problem.