# American Institute of Mathematical Sciences

October  2005, 13(5): 1277-1304. doi: 10.3934/dcds.2005.13.1277

## Moments and lower bounds in the far-field of solutions to quasi-geostrophic flows

 1 Department of Mathematics, University of Santa Cruz, Santa Cruz, CA 95064, United States 2 Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, United States

Received  August 2004 Revised  April 2005 Published  September 2005

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.

Citation: Maria Schonbek, Tomas Schonbek. Moments and lower bounds in the far-field of solutions to quasi-geostrophic flows. Discrete and Continuous Dynamical Systems, 2005, 13 (5) : 1277-1304. doi: 10.3934/dcds.2005.13.1277
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