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