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 L², up to a fractional logarithmic correction. As a corollary, we obtain the first local and global well-posedness results for initial free surfaces which are not Lipschitz.

中文翻译：

---

非Lipschitz初始数据的Muskat方程的柯西问题

摘要

本文致力于研究Muskat方程的Cauchy问题。我们考虑属于函数的临界 Sobolev 空间的初始数据，在L ^{2 中}具有三半导数，直到分数对数校正。作为推论，我们获得了非 Lipschitz 的初始自由表面的第一个局部和全局适定结果。