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January, 2010 Anisotropic L 2 -estimates of weak solutions to the stationary Oseen-type equations in 3D-exterior domain for a rotating body
Stanislav KRAČMAR, Šárka NEČASOVÁ, Patrick PENEL
J. Math. Soc. Japan 62(1): 239-268 (January, 2010). DOI: 10.2969/jmsj/06210239

Abstract

We study the Oseen problem with rotational effect in exterior three-dimensional domains. Using a variational approach we prove existence and uniqueness theorems in anisotropically weighted Sobolev spaces in the whole three-dimensional space. As the main tool we derive and apply an inequality of the Friedrichs-Poincaré type and the theory of Calderon-Zygmund kernels in weighted spaces. For the extension of results to the case of exterior domains we use a localization procedure.

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Stanislav KRAČMAR. Šárka NEČASOVÁ. Patrick PENEL. "Anisotropic L 2 -estimates of weak solutions to the stationary Oseen-type equations in 3D-exterior domain for a rotating body." J. Math. Soc. Japan 62 (1) 239 - 268, January, 2010. https://doi.org/10.2969/jmsj/06210239

Information

Published: January, 2010
First available in Project Euclid: 5 February 2010

zbMATH: 1186.35163
MathSciNet: MR2648222
Digital Object Identifier: 10.2969/jmsj/06210239

Subjects:
Primary: 35Q35
Secondary: 35B45 , 76D99

Keywords: anisotropically weighted $L^{2}$ spaces , Oseen problem , rotating body

Rights: Copyright © 2010 Mathematical Society of Japan

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Vol.62 • No. 1 • January, 2010
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