Analysis & PDE
- Anal. PDE
- Volume 12, Number 4 (2019), 997-1022.
Global well-posedness for the two-dimensional Muskat problem with slope less than 1
We prove the existence of global, smooth solutions to the two-dimensional Muskat problem in the stable regime whenever the product of the maximal and minimal slope is less than 1. The curvature of these solutions decays to 0 as goes to infinity, and they are unique when the initial data is . We do this by getting a priori estimates using a nonlinear maximum principle first introduced in a paper by Kiselev, Nazarov, and Volberg (2007), where the authors proved global well-posedness for the surface quasigeostraphic equation.
Anal. PDE, Volume 12, Number 4 (2019), 997-1022.
Received: 9 May 2017
Revised: 14 January 2018
Accepted: 30 July 2018
First available in Project Euclid: 30 October 2018
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Cameron, Stephen. Global well-posedness for the two-dimensional Muskat problem with slope less than 1. Anal. PDE 12 (2019), no. 4, 997--1022. doi:10.2140/apde.2019.12.997. https://projecteuclid.org/euclid.apde/1540864858