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

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 L2-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.