  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.
