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

On this paper spatial analyticity of solutions to the nonstationary incompressive Navier-Stokes flow in H˙n/2−1(Rn) is established. The proof is based on the 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→∞, as long as the solution exists. Although basic strategy is similar to our previous work with Giga for Ln space, one can make the proof short using several tools from harmonic analysis.