Partially congested propagation fronts in one-dimensional Navier-Stokes equations

TL;DR

This paper analyzes the behavior of solutions to the one-dimensional free-congested Navier-Stokes equations, focusing on existence, stability, and local well-posedness of certain profiles related to congestion phenomena.

Contribution

It provides the first local well-posedness result for the one-dimensional free-congested Navier-Stokes equations, building on previous work on existence and stability of congested profiles.

Findings

Existence of partially congested profiles

Asymptotic stability of these profiles

First local well-posedness result for the system

Abstract

These notes are dedicated to the analysis of the one-dimensional free-congested Navier-Stokes equations. After a brief synthesis of the results obtained in [4] related to the existence and the asymptotic stability of partially congested profiles associated to the soft congestion Navier-Stokes system, we present a first local well-posedness result for the one-dimensional free-congested Navier-Stokes equations.