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arXiv · 1110.6262

A gradient flow approach to a thin film approximation of the Muskat problem

Philippe Laurencot·Bogdan-Vasile Matioc
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Abstract

A fully coupled system of two second-order parabolic degenerate equations arising as a thin film approximation to the Muskat problem is interpreted as a gradient flow for the 2-Wasserstein distance in the space of probability measures with finite second moment. A variational scheme is then set up and is the starting point of the construction of weak solutions. The availability of two Liapunov functionals turns out to be a central tool to obtain the needed regularity to identify the Euler-Lagrange equation in the variational scheme.

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Philippe Laurencot, Bogdan-Vasile Matioc. 2011-10-28. A gradient flow approach to a thin film approximation of the Muskat problem. https://doi.org/10.1007/s00526-012-0520-5

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