Notes on the asymptotically self-similar singularities in the Euler and the Navier-Stokes equations

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December 2009, 25(4): 1181-1193. doi: 10.3934/dcds.2009.25.1181

Notes on the asymptotically self-similar singularities in the Euler and the Navier-Stokes equations

Dongho Chae ^1, , Kyungkeun Kang ^1, and Jihoon Lee ^1,

1.	Department of mathematics, Sungkyunkwan University, 300 Cheoncheon-dong, Jangan-gu, Suwon, 440-746, South Korea, South Korea

Received November 2008 Revised May 2009 Published September 2009

Abstract
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We exclude a type of asymptotically self-similar singularities which are the limiting cases of the results in [5] for the Euler and Navier-Stokes equations in dimension three.

Keywords: Euler equations, Navier-Stokes equations, self-similar singularity..

Mathematics Subject Classification: Primary: 35Q30, 35Q35; Secondary: 76Dxx, 76Bx.

Citation: Dongho Chae, Kyungkeun Kang, Jihoon Lee. Notes on the asymptotically self-similar singularities in the Euler and the Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2009, 25 (4) : 1181-1193. doi: 10.3934/dcds.2009.25.1181

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