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

Yong Zhou

doi:10.3934/dcds.2006.14.525

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2006, Volume 14, Issue 3: 525-532. Doi: 10.3934/dcds.2006.14.525

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

Yong Zhou^1,

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

Received: September 30, 2004

Revised: April 30, 2005

Published: August 2006

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Abstract

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:

Quasi-geostrophic ﬂows,
decay of solutions.

Mathematics Subject Classification: Primary: 35Q35; Secondary: 76D05.

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