On analyticity rate estimates of the solutions to the Navier--Stokes equations in Bessel-potential spaces (Q2573428)

Spatial analyticity of solutions to the nonstationary incompressible Navier-Stokes flow in \(\dot H^{n/2-1}(\mathbb R^n)\) is established. The proof is based on estimates for the higher order derivatives of solutions. These estimates imply not only the regularizing rates near \(t = 0\) but also decaying rates at \(t \to\infty,\) as long as the solution exists.