Free/Congested Two-Phase Model from Weak Solutions to Multi-Dimensional Compressible Navier-Stokes Equations

TL;DR

This paper extends the analysis of a two-phase compressible Navier-Stokes model with congestion constraints from one-dimensional to multi-dimensional cases, demonstrating convergence of solutions to a global weak solution.

Contribution

It generalizes previous one-dimensional results to multi-dimensional settings with heterogeneous density barriers, advancing the mathematical understanding of congested fluid flows.

Findings

Solutions converge to a global weak solution with congestion constraints

Extension from 1D to multi-dimensional models

Handles heterogeneous barriers in density

Abstract

We approximate a two--phase model by the compressible Navier-Stokes equations with a singular pressure term. Up to a subsequence, these solutions are shown to converge to a global weak solution of the compressible system with the congestion constraint studied for instance by P.L. Lions and N. Masmoudi [ Annales I.H.P., 1999]. The paper is an extension of the previous result obtained in one-dimensional setting by D. Bresch et al. [ C. R. Acad. Sciences Paris, 2014] to the multi-dimensional case with heterogeneous barrier for the density.