Stability of 2D incompressible flows in R3

We investigate the global in time stability of regular solutions with large velocity vectors to the evolutionary Navier–Stokes equation in R3. The class of stable flows contains all two-dimensional weak solutions. The only assumption which is required is smallness of the L2-norm of initial perturbation or its derivative with respect to the z-coordinate in the same norm. The magnitude of the rest of the norm of initial datum is not restricted.