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

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Numéro d'article	7
journal	Annals of PDE
Volume	7
Numéro de publication	1
Les DOIs	https://doi.org/10.1007/s40818-021-00099-x
état	Publié - 1 juin 2021
Modification externe	Oui

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10.1007/s40818-021-00099-x

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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\}",

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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.

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DO - 10.1007/s40818-021-00099-x

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JO - Annals of PDE

JF - Annals of PDE

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

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