Global well-posedness of the Navier–Stokes-omega equations

First, we prove that the local solution to the Navier–Stokes-omega equations is unique when the spatial dimension n satisfies 3 ≤ n ≤ 6 . Then, a regularity criterion is established for any n ≥ 3 . As a corollary, it is proved that the smooth solution exists globally when 3 ≤ n ≤ 6 .