Optimal convergence rates of the supercritical surface quasi-geostrophic equation

This study is concerned with the optimal convergence rates of the supercritical surface quasi-geostrophic equation. When the global weak solution θ of the supercritical surface quasi-geostrophic equation satisfies ∇θ∈Lr(0,∞;Ḃp,∞0(R2))for2p+αr=α,2α0.The findings are mainly based on some new estimates for the trilinear form in Besov spaces and the generalized Fourier splitting method.