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.
We have not been able to recognize your IP address
44.192.65.228
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.