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 nn satisfies 3≤n≤63≤n≤6. Then, a regularity criterion is established for any n≥3n≥3. As a corollary, it is proved that the smooth solution exists globally when 3≤n≤63≤n≤6.