Partial regularity for the Navier–Stokes equations with a force in a Morrey space

In the paper, we address the partial regularity of solutions of the Navier–Stokes system. Earlier, we have proved that the one-dimensional parabolic Hausdorff measure of the singular set is zero under the assumption that the force f belongs locally to L 5 / 3 . Here we prove the same statement under a more general assumption that the Morrey norm in L 5 / 7 10 / 7 of the force is sufficiently small. We do so by establishing a fractional integration theorem using the Morrey spaces and by a suitable iteration using a localized version of the Morrey norm.