Abstract
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 <p align="center"> $\frac{\partial \theta}{\partial t} + u\cdot \nabla \theta + \kappa (-\Delta)^{\alpha}\theta =f$, $\theta|_{t=0}=\theta_0 $ <p align="left" class="times">Rates of decay are obtained for moments of the solutions, and lower bounds of decay rates of the solutions are established. </span>
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