Convergence of approximating solutions of the Navier–Stokes equations in higher ordered Sobolev norms

Abstract We show that the approximating solutions of the Navier–Stokes equations constructed by Kato with the initial data converge to the local strong solution in the topology of for all provided the convergence in the scaling invariant norm in with the time weight holds. As an application of our convergence, it is clarified that the approximation of the pressure is established in .