论文标题
关于使用非lipschitz初始数据的Muskat方程的Cauchy问题
On the Cauchy problem for the Muskat equation with non-Lipschitz initial data
论文作者
论文摘要
本文致力于研究Muskat方程的Cauchy问题。我们考虑属于$ l^2 $的三半衍生物功能的关键Sobolev空间的初始数据，直至分数对数校正。作为推论，我们获得了不是Lipschitz的初始自由表面的第一个本地和全球适应性结果。
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 surface which are not Lipschitz.
