Global well-posedness for the two-dimensional Muskat problem with slope less than 1

By Stephen Cameron. Analysis & PDE, 2017

65 citations recorded by the source corpus.

We prove the existence of global, smooth solutions to the 2D Muskat problem in the stable regime whenever the initial data has slope strictly less than 1. The curvature of these solutions solutions decays to 0 as $t$ goes to infinity, and they are unique when the initial data is $C^{1,\epsilon}$. We do this by constructing a modulus of continuity generated by the equation, just as Kiselev, Nazarov, and Volberg did in their proof of the global well-posedness for the quasi-geostraphic equation.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/88b0ef879ea7e65d0b573cb38be6575d8c12755f

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In Applied Mathematics

1. Quoc-Hung Nguyen
2. Thomas Alazard

Citations in the corpus

• Endpoint Sobolev Theory for the Muskat Equation (2020, methodology): “Cameron, S.: Global well-posedness for the two-dimensional Muskat problem with slope less than 1.”