Calculus of Variations and Geometric Measure Theory
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T. Alazard - Q. H. Nguyen

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

created by nguyen on 03 Dec 2020

[BibTeX]

Submitted Paper

Inserted: 3 dec 2020

Year: 2020

ArXiv: 2009.04343 PDF

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 surface which are not Lipschitz.

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