Calculus of Variations and Geometric Measure Theory

T. Alazard - Q. H. Nguyen

On the Cauchy problem for the Muskat equation. II: Critical initial data

created by nguyen on 21 Feb 2021


Accepted Paper

Inserted: 21 feb 2021
Last Updated: 21 feb 2021

Journal: Annals of PDE
Year: 2021

ArXiv: 2009.08442 PDF


We prove that the Cauchy problem for the Muskat equation is well-posed locally in time for any initial data in the critical space of Lipschitz functions with three-half derivative in L2. Moreover, we prove that the solution exists globally in time under a smallness assumption.