# Homogenization of Stokes Systems and Uniform Regularity Estimates

@article{Gu2015HomogenizationOS,
title={Homogenization of Stokes Systems and Uniform Regularity Estimates},
author={Shu Gu and Zhongwei Shen},
journal={SIAM J. Math. Analysis},
year={2015},
volume={47},
pages={4025-4057}
}
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 $L^\infty$ estimates for the pressure as well as a Liouville property for solutions in $\mathbb{R}^d$. We also obtain the boundary $W^{1,p}$ estimates in a bounded $C^1$ domain for any \$1

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VIEW 2 EXCERPTS
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#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 23 REFERENCES

## Compactness methods in the theory of homogenization

VIEW 9 EXCERPTS
HIGHLY INFLUENTIAL

VIEW 4 EXCERPTS

## Nonlinear systems of the type of the stationary Navier–Stokes systems

M. Giaquinta, G Modica
• J. Reine Angew. Math.,
• 1982
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

VIEW 1 EXCERPT

VIEW 1 EXCERPT

W J. Geng
• Adv. Math.,
• 2012
VIEW 1 EXCERPT

VIEW 1 EXCERPT

VIEW 1 EXCERPT

## 1,p estimates for elliptic homogenization problems in nonsmooth domains

W Z. Shen
• Indiana Univ. Math. J.,
• 2008
VIEW 1 EXCERPT

• 2008
VIEW 1 EXCERPT