Global solvability of the Cauchy problem for the Navier–Stokes equation in for some class of initial data

In this paper we prove the existence of regular solutions to the Navier–Stokes equations if the initial data v 0 have some finite weighted norm and supp v 0 belongs to , is a ball with radius R 0 , where R 0 is sufficiently large. The proof follows from appropriate estimates in weighted Sobolev spaces.