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| We consider the steady-state Surface Quasi-Geostrophic equation in the whole space $\mathbb R^2$ driven by a forcing function $f$. The class of source functions $f$ under certain assumptions yield the existence of at least one solution with finite $L^2$ norm. These solutions are unique among all solutions with finite energy. The solutions are also shown to be stable in the following sense: If $\Theta$ is such a solution then any viscous, incompressible flow in the whole space, driven by $f$ and starting with finite energy, will return to $\Theta$. |
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