Rigorous thin film approximations of the one-phase unstable Muskat problem

Edoardo Bocchi; Francisco Gancedo

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arXiv · 2201.06015

Rigorous thin film approximations of the one-phase unstable Muskat problem

Edoardo Bocchi·Francisco Gancedo

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Abstract

This paper studies the one-phase Muskat problem driven by gravity and surface tension. The regime considered here is unstable with the fluid on top of a dry region. By a novel approach using a depth-averaged formulation, we derive two asymptotic approximations for this scenario. The lower order approximation is the classical thin film equation, while the higher order approximation provides a new refined thin film equation. We prove the optimal order of convergence in the shallowness parameter to the original Muskat solutions for both models with low-regular initial data.

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Edoardo Bocchi, Francisco Gancedo. 2022-01-16. Rigorous thin film approximations of the one-phase unstable Muskat problem. https://arxiv.org/abs/2201.06015

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