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

Dallas Albritton, Tobias Barker, Christophe Prange

Research output: Contribution to journalArticlepeer-review

Abstract

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 Lx3 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 Lx3 norm must concentrate at scales ∼T−t in the presence of a Type I blow-up.

Original languageEnglish
Article number109729
JournalJournal of Functional Analysis
Volume284
Issue number1
Early online date4 Oct 2022
DOIs
Publication statusE-pub ahead of print - 4 Oct 2022

Keywords

  • Epsilon regularity
  • Navier-Stokes equations

ASJC Scopus subject areas

  • Analysis

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