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Uniqueness of the exact solutions of the Navier—Stokes equations having null nonlinearity

Published online by Cambridge University Press:  12 July 2007

Sun-Chul Kim  and
Hisashi Okamoto
Sun-Chul Kim
Affiliation:
Department of Mathematics, Chung-Ang University, 221 Heukseok-dong, Dongjak-ku, Seoul 156-756, Korea
Hisashi Okamoto
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502 Japan (okamoto@kurims.kyoto-u.ac.jp)
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Abstract

We consider an overdetermined system of elliptic partial differential equations arising in the Navier–Stokes equations. This analysis enables us to prove that the well-known classical solutions such as Couette flows and others are the only solutions that satisfy both the stationary Navier–Stokes and Euler equations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 6 , December 2006 , pp. 1303 - 1315
Copyright
Copyright © Royal Society of Edinburgh 2006

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