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Asymptotic stability of the critical and super-critical dissipative quasi-geostrophic equation

The asymptotic stability for the weak solution θ of the critical and supercritical dissipative quasi-geostrophic equation in the Serrin-type class ∇θ ∊ Lr(0, ∞;Lp(R2)) is examined. This equation is perturbed by large initial data and external functions. It is shown that every weak perturbed solution has the same asymptotic behaviour as that of θ. More precisely, the difference decays in the norm of L2(R2).