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Article Dans Une Revue Journal of the Mathematical Society of Japan Année : 2014

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

Résumé

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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Dates et versions

hal-00711478 , version 1 (25-06-2012)

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Philippe Laurencot, Bogdan-Vasile Matioc. A thin film approximation of the Muskat problem with gravity and capillary forces. Journal of the Mathematical Society of Japan, 2014, 66, pp.1043-1071. ⟨10.2969/jmsj/06641043⟩. ⟨hal-00711478⟩
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