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arXiv · 1209.1575

The confined Muskat problem: differences with the deep water regime

Diego Córdoba Gazolaz·Rafael Granero-Belinchón·Rafael Orive Illera
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Abstract

We study the evolution of the interface given by two incompressible fluids with different densities in the porous strip $\RR\times[-l,l]$. This problem is known as the Muskat problem and is analogous to the two phase Hele-Shaw cell. The main goal of this paper is to compare the qualitative properties between the model when the fluids move without boundaries and the model when the fluids are confined. We find that, in a precise sense, the boundaries decrease the diffusion rate and the system becomes more singular.

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Diego Córdoba Gazolaz, Rafael Granero-Belinchón, Rafael Orive Illera. 2013-01-18. The confined Muskat problem: differences with the deep water regime. https://arxiv.org/abs/1209.1575

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