Decay rate of higher order derivatives for solutions to the 2-D dissipative quasi-geostrophic flows (Q867393)

The author derives the title estimates in \(L^2\)-norm for the equations without forcing term. Under the additional assumption that the solution does not strongly deviate from the solution of the corresponding linear equations with the same initial data, the author is able to obtain lower and upper bounds on the decay. Instead of the usual Fourier splitting method applied to similar problems by many previous authors, here the main idea of the proof is based on Gevrey estimates.