Author:
Albritton Dallas,Barker Tobias,Prange Christophe
Abstract
AbstractWe give a new concise proof of a certain one-scale epsilon regularity criterion using weak-strong uniqueness for solutions of the Navier–Stokes equations with non-zero boundary conditions. It is inspired by an analogous approach for the stationary system due to Struwe.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Condensed Matter Physics,Mathematical Physics
Reference29 articles.
1. Albritton, D., Dong, H.: Regularity properties of passive scalars with rough divergence-free drifts. arXiv preprint arXiv:2107.12511 (2021)
2. Barker, T., Prange, C.: Localized smoothing for the Navier–Stokes equations and concentration of critical norms near singularities. Arch. Ration. Mech. Anal. 236(3), 1487–1541 (2020)
3. Caffarelli, L., Kohn, R., Nirenberg, L.: Partial regularity of suitable weak solutions of the Navier–Stokes equations. Commun. Pure Appl. Math. 35(6), 771–831 (1982)
4. Droniou, J.: Quelques Résultats sur les Espaces de Sobolev. Working paper or preprint (2001)
5. Escauriaza, L., Seregin, G.A., Šverák, V.: $$L_{3,\infty }$$-solutions of Navier–Stokes equations and backward uniqueness. Uspekhi Mat. Nauk. 58(2), 3–44 (2003)