Analyticity of the subcritical and critical quasi-geostrophic equations in Besov spaces, preprint

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 [23]. We show that mild solutions are Gevrey regular, i.e. they satisfy the estimate sup t>0 ‖eαt1/γΛ1θ(t)‖L <∞ for a suitably chosen α> 0 and a scaling invariant Besov space L. 1 Introduction and statement of main results In this paper, we study analyticity properties of the dissipative quasi-geostrophic equations. These equations are derived from the more general quasi-geostrophic approximation for a rapidly rotat-ing non-homogeneous fluid flow with small Rossby and Ekman numbers. For the case of special solutions with constant potential vorticity in the interior and constant buoyancy frequency (nor