Moments and lower bounds in the far-field of solutions to quasi-geostrophic flows
Maria Schonbek Tomas Schonbek
Discrete & Continuous Dynamical Systems - A 2005, 13(5): 1277-1304 doi: 10.3934/dcds.2005.13.1277
We consider the long time behavior of moments of solutions and of the solutions itself to dissipative Quasi-Geostrophic flow (QG) with sub-critical powers. The flow under consideration is described by the nonlinear scalar equation

$\frac{\partial \theta}{\partial t} + u\cdot \nabla \theta + \kappa (-\Delta)^{\alpha}\theta =f$, $\theta|_{t=0}=\theta_0 $

Rates of decay are obtained for moments of the solutions, and lower bounds of decay rates of the solutions are established.

keywords: Fourier-splitting. decay Quasi-geostrophic

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