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Decay rate of higher order derivatives for solutions to the 2-D dissipative quasi-geostrophic flows. (English) Zbl 1185.35203
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.
MSC:
35Q35PDEs in connection with fluid mechanics
76U05Rotating fluids
86A05Hydrology, hydrography, oceanography