Localized smoothing and concentration for the Navier-Stokes equations in the half space

We establish a local-in-space short-time smoothing effect for the Navier-Stokes equations in half space. The whole space analogue, due to Jia and Šverák [21], is central tool two of authors' recent work on quantitative Lx3 blow-up criteria [7]. main difficulty that non-local effects pressure are much stronger than As an application, we demonstrate critical norm must concentrate at scales ∼T⁎−t presence Type I blow-up.