Accepted Paper

Inserted: 3 dec 2020
Last Updated: 6 aug 2021

Journal: Com. PDE
Year: 2020

Abstract:

This article is devoted to the study of the Cauchy problem for the Muskat equation. We consider initial data belonging to the critical Sobolev space of functions with three-half derivative in L^2, up to a fractional logarithmic correction. As a corollary, we obtain the first local and global well-posedness results for initial free surface which are not Lipschitz.