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

Thomas Alazard; Quoc Hung Nguyen

doi:10.1080/03605302.2021.1928700

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

Thomas Alazard
, Quoc Hung Nguyen

Research output: Contribution to journal › Article › peer-review

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 surfaces which are not Lipschitz.

Original language	English
Pages (from-to)	2171-2212
Number of pages	42
Journal	Communications in Partial Differential Equations
Volume	46
Issue number	11
DOIs	https://doi.org/10.1080/03605302.2021.1928700
Publication status	Published - 1 Jan 2021
Externally published	Yes

Keywords

Critical Cauchy problem
Darcy
free boundary flow

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10.1080/03605302.2021.1928700

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title = "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 surfaces which are not Lipschitz.",

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AU - Nguyen, Quoc Hung

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AB - 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.

KW - Critical Cauchy problem

KW - Darcy

KW - free boundary flow

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DO - 10.1080/03605302.2021.1928700

M3 - Article

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JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 11

ER -

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

Abstract

Keywords

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