On perturbations of solutions to the Navier–Stokes equations with large initial data and their dynamics

Abstract We prove a theorem on stability of a strong solution of the Navier–Stokes equation with respect to perturbation of the initial velocity in the norm of D ( A 1 / 4 ) (where A is the Stokes operator) and also with respect to certain perturbations of the acting body force. The theorem is applied to obtain new results on the dynamics of solutions of the Navier–Stokes equations.