On the Cauchy Problem for the Muskat Equation. II: Critical Initial Data

Thomas Alazard; Quoc Hung Nguyen

doi:10.1007/s40818-021-00099-x

On the Cauchy Problem for the Muskat Equation. II: Critical Initial Data

Thomas Alazard
, Quoc Hung Nguyen

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

Abstract

We prove that the Cauchy problem for the Muskat equation is well-posed locally in time for any initial data in the critical space of Lipschitz functions with three-half derivative in L². Moreover, we prove that the solution exists globally in time under a smallness assumption.

Original language	English
Article number	7
Journal	Annals of PDE
Volume	7
Issue number	1
DOIs	https://doi.org/10.1007/s40818-021-00099-x
Publication status	Published - 1 Jun 2021
Externally published	Yes

Access to Document

10.1007/s40818-021-00099-x

Cite this

@article{5501102a4cee4a30852a30babb06e886,

title = "On the Cauchy Problem for the Muskat Equation. II: Critical Initial Data",

abstract = "We prove that the Cauchy problem for the Muskat equation is well-posed locally in time for any initial data in the critical space of Lipschitz functions with three-half derivative in L2. Moreover, we prove that the solution exists globally in time under a smallness assumption.",

author = "Thomas Alazard and Nguyen, \{Quoc Hung\}",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2021",

month = jun,

day = "1",

doi = "10.1007/s40818-021-00099-x",

language = "English",

volume = "7",

journal = "Annals of PDE",

issn = "2524-5317",

number = "1",

}

TY - JOUR

T1 - On the Cauchy Problem for the Muskat Equation. II

T2 - Critical Initial Data

AU - Alazard, Thomas

AU - Nguyen, Quoc Hung

PY - 2021/6/1

Y1 - 2021/6/1

N2 - We prove that the Cauchy problem for the Muskat equation is well-posed locally in time for any initial data in the critical space of Lipschitz functions with three-half derivative in L2. Moreover, we prove that the solution exists globally in time under a smallness assumption.

AB - We prove that the Cauchy problem for the Muskat equation is well-posed locally in time for any initial data in the critical space of Lipschitz functions with three-half derivative in L2. Moreover, we prove that the solution exists globally in time under a smallness assumption.

U2 - 10.1007/s40818-021-00099-x

DO - 10.1007/s40818-021-00099-x

M3 - Article

AN - SCOPUS:85102830879

SN - 2524-5317

VL - 7

JO - Annals of PDE

JF - Annals of PDE

IS - 1

M1 - 7

ER -

On the Cauchy Problem for the Muskat Equation. II: Critical Initial Data

Abstract

Access to Document

Fingerprint

Cite this