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We study the critical dissipative quasi-geostrophic equations in $\bR^2$ witharbitrary $H^1$ initial data. After showing certain decay estimate, a globalwell-posedness result is proved by adapting the method in [11] with a suitablemodification. A decay in time estimate for higher order homogeneous Sobolevnorms of solutions is also discussed.

Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space