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arXiv · 1603.03949

On the Two-Dimensional Muskat Problem with Monotone Large Initial Data

Fan Deng·Zhen Lei·Fanghua Lin
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Abstract

We consider the evolution of two incompressible, immiscible fluids with different densities in porous media, known as the Muskat problem [21], which in two dimensions is analogous to the Hele-Shaw cell [26]. We establish, for a class of large and monotone initial data, the global existence of weak solutions. The proof is based on a local well-posedness result for the initial data with certain specific asymptotics at spatial infinity and a new maximum principle for the first derivative of the graph function.

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Fan Deng, Zhen Lei, Fanghua Lin. 2016-03-12. On the Two-Dimensional Muskat Problem with Monotone Large Initial Data. https://arxiv.org/abs/1603.03949

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