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

Anne-Laure Dalibard (1) , Charlotte Perrin

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

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.

Mots clés: Navier-Stokes equations; free boundary problem; traveling waves; nonlinear stability.; MSC: 35Q35; 35L67

Domaines: Equations aux dérivées partielles [math.AP]

Anne-Laure Dalibard, Charlotte Perrin. Partially congested propagation fronts in one-dimensional Navier-Stokes equations. Journal of Elliptic and Parabolic Equations, 2021. ⟨hal-03213754⟩