Decay rate of higher order derivatives for solutions to the 2-D dissipative quasi-geostrophic flows

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July 2006, 14(3): 525-532. doi: 10.3934/dcds.2006.14.525

Decay rate of higher order derivatives for solutions to the 2-D dissipative quasi-geostrophic flows

1.	Department of Mathematics, East China Normal University, Shanghai 200062

Received October 2004 Revised May 2005 Published December 2005

Abstract
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In this paper we derive a decay rate of higher order derivatives for solutions to the 2-D dissipative quasi-geostrophic flows under the condition that the $L^2$-norm itself decays. Moreover, under an additional assumption that the solution stays sufficiently close to that of the corresponding linear equation, then both lower bounds and upper bounds on the decay of higher derivatives are obtained.

Keywords: decay of solutions., Quasi-geostrophic ﬂows.

Mathematics Subject Classification: Primary: 35Q35; Secondary: 76D0.

Citation: Yong Zhou. Decay rate of higher order derivatives for solutions to the 2-D dissipative quasi-geostrophic flows. Discrete & Continuous Dynamical Systems - A, 2006, 14 (3) : 525-532. doi: 10.3934/dcds.2006.14.525

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