Asymptotic profiles of solutions to the 2D viscous incompressible  micropolar fluid flows

Bo-Qing Dong; Zhi-Min Chen

doi:10.3934/dcds.2009.23.765

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2009, Volume 23, Issue 3: 765-784. Doi: 10.3934/dcds.2009.23.765

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Asymptotic profiles of solutions to the 2D viscous incompressible micropolar fluid flows

Bo-Qing Dong^1, and
Zhi-Min Chen^2,

1.
School of Mathematical Sciences, Anhui University, Hefei,Anhui 230039
2.
School of Engineering Sciences, University of Southampton, Southampton SO17 1BJ

Received: May 31, 2007

Revised: July 31, 2008

Published: August 2009

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Abstract

This paper deals with asymptotic profiles of solutions to the 2D viscous incompressible micropolar fluid flows in the whole space $R^2$. Based on the spectral decomposition of linearized micropolar fluid flows, the sharp algebraic time decay estimates of the micropolar fluid flows in $L_2$ and $L_\infty$ norms are obtained.

Keywords:

micropolar fluid flows; spectral decomposition; asymptotic profiles.

Mathematics Subject Classification: Primary: 35B40, 35Q35,76D03; Secondary: 35Q30, 76A05,76D05.

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