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

摘要

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?Dalibard and Perrin (Commun Math Sci 18(7):1775–1813, 2020) 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.