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The initial value problem for the two dimensional dissipativequasi-geostrophic equation derived from geophisical fluid dynamics is studied.The dissipation of this equation is given by the fractional Laplacian. It isknown that the half Laplacian is a critical dissipation for thequasi-geostrophic equation. In this paper, far field asymptotics of solutionsare given in the critical and the supercritical cases.

Spatial-decay of solutions to the quasi-geostrophic equation with the critical and the super-critical dissipation