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 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.
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