# American Institute of Mathematical Sciences

September  2004, 3(3): 433-446. doi: 10.3934/cpaa.2004.3.433

## Kwak transformation and Navier-Stokes equations

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

Received  May 2003 Revised  March 2004 Published  June 2004

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.
Citation: Hyukjin Kwean. Kwak transformation and Navier-Stokes equations. Communications on Pure & Applied Analysis, 2004, 3 (3) : 433-446. doi: 10.3934/cpaa.2004.3.433
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