Analyticity of the Subcritical and Critical Quasi-Geostrophic equations in Besov Spaces

We establish analyticity of the subcritical and critical quasi-geostrophic equations in critical Besov spaces. The main method is so-called Gevrey estimates, which is motivated by the work of Foias and Temam. We show that mild solutions \theta(t), are Gevrey regular, i.e. they satisfy the estimate \sup_{t>0}\|e^{\alpha t^{1/\gamma}\Lambda_1}\theta(t)\|_{\cap L}<\infty. for a suitably chosen \alpha>0 and a scaling invariant Besov space {\cap L}.