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

Dallas Albritton, Tobias Barker, Christophe Prange

OAI: oai:purehost.bath.ac.uk:openaire_cris_publications/6f1537c5-3ed9-47ec-a778-878796b19e90 • DOI: https://doi.org/10.1016/j.jfa.2022.109729

We establish a local-in-space short-time smoothing effect for the Navier-Stokes equations in the half space. The whole space analogue, due to Jia and Šverák [21], is a central tool in two of the authors' recent work on quantitative L_x³ blow-up criteria [7]. The main difficulty is that the non-local effects of the pressure in the half space are much stronger than in the whole space. As an application, we demonstrate that the critical L_x³ norm must concentrate at scales ∼T^⁎−t in the presence of a Type I blow-up.

Epsilon regularity Navier-Stokes equations /dk/atira/pure/subjectarea/asjc/2600/2603 name=Analysis