On the Cauchy problem for the Muskat equation with non-Lipschitz initial data
On the Cauchy problem for the Muskat equation with non-Lipschitz initial data
复制标题
DOI：
10.1080/03605302.2021.1928700
复制
发表时间：
2021-05-13
影响因子：
1.9
通讯作者：
Nguyen, Quoc-Hung
中科院分区：
文献类型：
--
作者：
Alazard, Thomas;Nguyen, Quoc-Hung
本文主要研究Muskat方程的柯西问题。我们考虑初始数据属于临界Sobolev空间的函数在L-2中具有三-二分之一的导数，直到分数对数校正。作为推论，我们得到了非Lipschitz初始自由曲面的第一个局部适定性和全局适定性结果。
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 surfaces which are not Lipschitz.