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

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 ${\dot{B}}_{p,q}^{3\mathrm{/}p-1}$. 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.