From concentration to quantitative regularity: a short survey of recent developments for the Navier-Stokes equations - Archive ouverte HAL
Article Dans Une Revue Vietnam Journal of Mathematics Année : 2022

From concentration to quantitative regularity: a short survey of recent developments for the Navier-Stokes equations

Résumé

In this short survey paper, we focus on some new developments in the study of the regularity or potential singularity formation for solutions of the 3D Navier-Stokes equations. Some of the motivating questions are: Are certain norms accumulating/concentrating on small scales near potential blow-up times? At what speed do certain scale-invariant norms blow-up? Can one prove explicit quantitative regularity estimates? Can one break the criticality barrier, even slightly? We emphasize that these questions are closely linked together. Many recent advances for the Navier-Stokes equations are directly inspired by results and methods from the field of nonlinear dispersive equations.

Dates et versions

hal-04337134 , version 1 (12-12-2023)

Identifiants

Citer

Tobias Barker, Christophe Prange. From concentration to quantitative regularity: a short survey of recent developments for the Navier-Stokes equations. Vietnam Journal of Mathematics, In press, ⟨10.48550/ARXIV.2211.16215⟩. ⟨hal-04337134⟩
14 Consultations
0 Téléchargements

Altmetric

Partager

More