On the Cauchy problem for the Muskat equation. II: Critical initial data
Analysis of PDEs
2021-03-04 v2
Abstract
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 . Moreover, we prove that the solution exists globally in time under a smallness assumption.
Keywords
Cite
@article{arxiv.2009.08442,
title = {On the Cauchy problem for the Muskat equation. II: Critical initial data},
author = {Thomas Alazard and Quoc-Hung Nguyen},
journal= {arXiv preprint arXiv:2009.08442},
year = {2021}
}
Comments
This is a sequel to our previous paper arXiv:2009.04343