A thin film approximation of the Muskat problem with gravity and capillary forces

2012/06/25 by Philippe Laurençot, Laurencot, Philippe, Bogdan–Vasile Matioc +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.1206.5600

openalex publication_date 2012/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Existence of nonnegative weak solutions is shown for a thin film approximation of the Muskat problem with gravity and capillary forces taken into account. The model describes the space-time evolution of the heights of the two fluid layers and is a fully coupled system of two fourth order degenerate parabolic equations. The existence proof relies on the fact that this system can be viewed as a gradient flow for the 2-Wasserstein distance in the space of probability measures with finite second moment.

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