On the Cauchy problem for the Muskat equation with non-Lipschitz initial data

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 $L^2$, 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.

41 pages

References in corpus (1)

• Regularity for a special case of two-phase Hele-Shaw flow via parabolic integro-differential equations