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Applicable Analysis
An International Journal
Volume 89, 2010 - Issue 1
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Original Articles

Asymptotic analysis of the Stokes problem on general bounded domains: the case of a characteristic boundary

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Pages 49-66 | Received 22 Jul 2009, Accepted 09 Oct 2009, Published online: 19 Jan 2010
 

Abstract

The goal of this article is to study the asymptotic behaviour of the solutions of linearized Navier–Stokes equations (LNSE), when the viscosity is small, in a general (curved) bounded and smooth domain in ℝ3 with a characteristic boundary. To handle the difficulties due to the curvature of the boundary, we first introduce a curvilinear coordinate system which is adapted to the boundary. Then we prove the existence of a strong corrector for the LNSE. More precisely, we show that the solution of LNSE behaves like the corresponding Euler solution except in a thin region, near the boundary, where a certain heat solution is added as a corrector.

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Acknowledgements

This work was supported in part by NSF grants DMS 0604235 and 0906440, and by the Research Fund of Indiana University.

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