Space-time analyticity and refined analyticity radius of the Navier-Stokes equations in the critical Besov spaces

Abstract

In this paper, we establish the space-time analyticity of global solutions to the incompressible Navier-Stokes equations with small initial data in critical \emph{Besov} spaces $\dot B^{3/p-1}_{p,q}$. Time decay rates of higher order space-time joint derivatives and instantaneous lower bounds of the analyticity radius follow as straightforward consequences. The method employed combines Gevrey-class estimates with iterative derivative techniques. Furthermore, we obtain a logarithmic improvement in the lower bound for the spatial analyticity radius of solutions for arbitrary initial data in critical \emph{Besov} spaces.