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arXiv · 1206.5600

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

Philippe Laurencot·Bogdan-Vasile Matioc
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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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Philippe Laurencot, Bogdan-Vasile Matioc. 2012-06-25. A thin film approximation of the Muskat problem with gravity and capillary forces. https://arxiv.org/abs/1206.5600

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