Global existence of solutions for a multi-phase flow: a drop in a gas-tube

TL;DR

This paper proves the global existence of weak solutions for a hyperbolic system modeling a three-phase inviscid fluid flow with stationary interfaces, addressing large initial data scenarios.

Contribution

It establishes the first global existence result for a multi-phase flow model with stationary interfaces in a hyperbolic conservation law framework.

Findings

Proved global existence of weak entropic solutions.

Validated the model for large initial data.

Demonstrated stability of solutions over time.

Abstract

In this paper we study the flow of an inviscid fluid composed by three different phases. The model is a simple hyperbolic system of three conservation laws, in Lagrangian coordinates, where the phase interfaces are stationary. Our main result concerns the global existence of weak entropic solutions to the initial-value problem for large initial data.