Kwak transformation and Navier-Stokes equations

Hyukjin Kwean

doi:10.3934/cpaa.2004.3.433

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2004, Volume 3, Issue 3: 433-446. Doi: 10.3934/cpaa.2004.3.433

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Kwak transformation and Navier-Stokes equations

Hyukjin Kwean^1,

1.
Department of Mathematics Education, Korea University, 1, 5-ka Anam-dong Sungbuk- ku, Seoul, 136-701

Received: April 30, 2003

Revised: February 29, 2004

Published: August 2004

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Abstract

In this paper we study the asymptotic dynamics of the 2-dimensional Navier-Stokes equations on a bounded domain $\Omega \subset R^2$ with the mixed-free boundary conditions. We prove that there exists a system of reaction-diffusion equations which possesses exactly the same asymptotic dynamics as the Navier-Stokes equations.

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Mathematics Subject Classification: Primary 35Q30; Secondary 35K57, 34B40, 76D05.

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