Homogenization of stokes systems and uniform regularity estimates

Shu Gu; Zhongwei Shen

doi:10.1137/151004033

Homogenization of stokes systems and uniform regularity estimates

Shu Gu
, Zhongwei Shen

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

29 Scopus citations

Abstract

This paper is concerned with uniform regularity estimates for a family of Stokes systems with rapidly oscillating periodic coefficients. We establish interior Lipschitz estimates for the velocity and L^∞ estimates for the pressure as well as a Liouville property for solutions in ℝ^d. We also obtain the boundary W^1,p estimates in a bounded C¹ domain for any 1 p ∞.

Original language	English
Pages (from-to)	4025-4057
Number of pages	33
Journal	SIAM Journal on Mathematical Analysis
Volume	47
Issue number	5
DOIs	https://doi.org/10.1137/151004033
State	Published - 2015

Bibliographical note

Publisher Copyright:
© 2015 Society for Industrial and Applied Mathematics.

Funding

Funders	Funder number
National Stroke Foundation	DMS-1161154
National Stroke Foundation

Keywords

Homogenization
Regularity
Stokes systems

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/151004033

Cite this

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title = "Homogenization of stokes systems and uniform regularity estimates",

abstract = "This paper is concerned with uniform regularity estimates for a family of Stokes systems with rapidly oscillating periodic coefficients. We establish interior Lipschitz estimates for the velocity and L∞ estimates for the pressure as well as a Liouville property for solutions in ℝd. We also obtain the boundary W1,p estimates in a bounded C1 domain for any 1 p ∞.",

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author = "Shu Gu and Zhongwei Shen",

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year = "2015",

doi = "10.1137/151004033",

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T1 - Homogenization of stokes systems and uniform regularity estimates

AU - Gu, Shu

AU - Shen, Zhongwei

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N2 - This paper is concerned with uniform regularity estimates for a family of Stokes systems with rapidly oscillating periodic coefficients. We establish interior Lipschitz estimates for the velocity and L∞ estimates for the pressure as well as a Liouville property for solutions in ℝd. We also obtain the boundary W1,p estimates in a bounded C1 domain for any 1 p ∞.

AB - This paper is concerned with uniform regularity estimates for a family of Stokes systems with rapidly oscillating periodic coefficients. We establish interior Lipschitz estimates for the velocity and L∞ estimates for the pressure as well as a Liouville property for solutions in ℝd. We also obtain the boundary W1,p estimates in a bounded C1 domain for any 1 p ∞.

KW - Homogenization

KW - Regularity

KW - Stokes systems

UR - https://www.scopus.com/pages/publications/84947460423

UR - https://www.scopus.com/pages/publications/84947460423#tab=citedBy

U2 - 10.1137/151004033

DO - 10.1137/151004033

M3 - Article

AN - SCOPUS:84947460423

SN - 0036-1410

VL - 47

SP - 4025

EP - 4057

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 5

ER -

Homogenization of stokes systems and uniform regularity estimates

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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