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

Philippe Laurencot1, Bogdan-Vasile Matioc2

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.

1:	IMT - Institut de Mathématiques de Toulouse
2:	Institut für Mathematik

Keyword(s) : thin film – degenerate parabolic system – gradient flow – Wasserstein distance

hal-00711478, version 1

http://hal.archives-ouvertes.fr/hal-00711478

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From: Philippe Laurencot <>

Submitted on: Monday, 25 June 2012 09:32:37

Updated on: Monday, 25 June 2012 10:02:13