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

摘要

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 L5/3. Here we prove the same statement under a more general assumption that the Morrey norm in L5/710/7 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.