It is known that near blowup time, the critical norms of strong solutions blow up. At this time, strong solutions cease to exist. However, sw-solutions (or local energy solutions in general) remain in local energy space and coincide the strong solution up to the blowup time. In recent years, a large volume of literature on local regularity near blowup time has been published, including the work of D. Albritton and T. Barker (2018), H. Jia and V. Sverak (2013), W. Rusin and V. Sverak (2011). I will give a brief overview of these works and their connections to the problem of minimal data for potential Navier-Stokes singularities in the half-space.