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

Mathematics

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

26 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.

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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doi = "10.1137/151004033",

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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

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DO - 10.1137/151004033

M3 - Article

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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

Keywords

ASJC Scopus subject areas

Access to Document

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