Compactness and large-scale regularity for Darcy's law

Zhongwei Shen

doi:10.1016/j.matpur.2022.05.019

Compactness and large-scale regularity for Darcy's law

Zhongwei Shen

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

5 Scopus citations

Abstract

This paper is concerned with the quantitative homogenization of the steady Stokes equations with the Dirichlet condition in a periodically perforated domain. Using a compactness method, we establish the large-scale interior C^1,α and Lipschitz estimates for the velocity as well as the corresponding estimates for the pressure. These estimates, when combined with the classical regularity estimates for the Stokes equations, yield the uniform Lipschitz estimates. As a consequence, we also obtain the uniform W^k,p estimates for 1<p<∞.

Original language	English
Pages (from-to)	673-701
Number of pages	29
Journal	Journal des Mathematiques Pures et Appliquees
Volume	163
DOIs	https://doi.org/10.1016/j.matpur.2022.05.019
State	Published - Jul 2022

Bibliographical note

Publisher Copyright:
© 2022 Elsevier Masson SAS

Funding

Supported in part by NSF grant DMS-1856235.

Funders	Funder number
National Science Foundation Arctic Social Science Program	DMS-1856235

Keywords

Darcy law
Large-scale regularity
Perforated domain
Stokes equations

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1016/j.matpur.2022.05.019

Cite this

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title = "Compactness and large-scale regularity for Darcy's law",

abstract = "This paper is concerned with the quantitative homogenization of the steady Stokes equations with the Dirichlet condition in a periodically perforated domain. Using a compactness method, we establish the large-scale interior C1,α and Lipschitz estimates for the velocity as well as the corresponding estimates for the pressure. These estimates, when combined with the classical regularity estimates for the Stokes equations, yield the uniform Lipschitz estimates. As a consequence, we also obtain the uniform Wk,p estimates for 1",

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N2 - This paper is concerned with the quantitative homogenization of the steady Stokes equations with the Dirichlet condition in a periodically perforated domain. Using a compactness method, we establish the large-scale interior C1,α and Lipschitz estimates for the velocity as well as the corresponding estimates for the pressure. These estimates, when combined with the classical regularity estimates for the Stokes equations, yield the uniform Lipschitz estimates. As a consequence, we also obtain the uniform Wk,p estimates for 1

AB - This paper is concerned with the quantitative homogenization of the steady Stokes equations with the Dirichlet condition in a periodically perforated domain. Using a compactness method, we establish the large-scale interior C1,α and Lipschitz estimates for the velocity as well as the corresponding estimates for the pressure. These estimates, when combined with the classical regularity estimates for the Stokes equations, yield the uniform Lipschitz estimates. As a consequence, we also obtain the uniform Wk,p estimates for 1

KW - Darcy law

KW - Large-scale regularity

KW - Perforated domain

KW - Stokes equations

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JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

ER -

Compactness and large-scale regularity for Darcy's law

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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