# A general existence result for isothermal two-phase flows with phase transition

## TL;DR

This paper extends the mathematical analysis of isothermal two-phase flows with phase transitions to more general substances and equations of state, proving existence and uniqueness of solutions for Riemann problems.

## Contribution

It generalizes previous results to arbitrary substances and equations of state, establishing fundamental existence and uniqueness theorems for these flows.

## Key findings

- Proved existence and uniqueness for Riemann problems in generalized settings.
- Discussed nucleation and evaporation phenomena.
- Extended analytical framework beyond linear equations of state.

## Abstract

Liquid-vapor flows with phase transitions have a wide range of applications. Isothermal two-phase flows described by a single set of isothermal Euler equations, where the mass transfer is modeled by a kinetic relation, have been investigated analytically in (Quarterly of applied Mathematics, vol.\ LXXI 3 (2013), pp.\ 509-540.). This work was restricted to liquid water and its vapor modeled by linear equations of state. The focus of the present work lies on the generalization of the primary results to arbitrary substances, arbitrary equations of state and thus a more general kinetic relation. We prove existence and uniqueness results for Riemann problems. In particular, nucleation and evaporation are discussed.