Calculus of Variations and Geometric Measure Theory

T. Alazard - Q. H. Nguyen

On the Cauchy problem for the Muskat equation with non-Lipschitz initial data

created by nguyen on 03 Dec 2020
modified on 06 Aug 2021


Accepted Paper

Inserted: 3 dec 2020
Last Updated: 6 aug 2021

Journal: Com. PDE
Year: 2020

ArXiv: 2009.04343 PDF


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 L2, 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.