Well-Posedness and Analyticity for Quasi-Geostrophic Equation in the Besov-Morrey Spaces characterized by Semi-Group

Abstract

In this work we showed the existence and uniqueness, the analyticity of the solutions and the decay estimates of the solutions of the quasi-geostrophic equation (QG) in the Besov-Morrey spaces carterized by semigroup $\mathrm{T}_{\alpha}:=e^{-t (-\Delta)^{\alpha}}$, noted by $\mathrm{N}_{p,\lambda}^{s}$. If we assume that the initial data $\theta_0$ are small and belong to the Besov-Morrey critical spaces, we obtain the global well-posedness results of the QG equation.