Analyticity and Decay Estimates of the Navier-Stokes Equations in Critical Besov Spaces

In this paper, we establish analyticity of the Navier-Stokes equations with small data in critical Besov spaces . The main method is Gevrey estimates, the choice of which is motivated by the work of Foias and Temam (Contemp Math 208:151-180, 1997). We show that mild solutions are Gevrey regular, that is, the energy bound holds in , globally in time for p < a. We extend these results for the intricate limiting case p = a in a suitably designed E (a) space. As a consequence of analyticity, we obtain decay estimates of weak solutions in Besov spaces. Finally, we provide a regularity criterion in Besov spaces.