Asymptotic study of supercritical surface Quasi-Geostrophic equation in critical space

In this paper we prove, if $θ\in C([0,\infty),H^{2-2α}(\mathbb R^2))$ is a global solution of supercritical surface Quasi-Geostrophic equation with small initial data, then $\|θ(t)\|_{H^{2-2α}}$ decays to zero as time goes to infinity. Fourier analysis and standard techniques are used.

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