Quantitative robustness of regularity for 3D Navier-Stokes system in $\dot H^\alpha$-spaces

TL;DR

This paper investigates the stability and regularity of the 3D Navier-Stokes equations in specific Sobolev spaces, providing explicit quantitative results and analyzing scaling properties in a periodic setting.

Contribution

It offers new quantitative stability and regularity results for the 3D Navier-Stokes system in $ ext{dot} H^eta$ spaces with explicit constants and scaling analysis.

Findings

Quantitative stability results with explicit constants

Regularity criteria in $ ext{dot} H^eta$ spaces for $eta ext{ in } [1/2,1]$

Analysis of scaling properties in periodic domains

Abstract

We present stability and regularity results for the $3$D incompressible Navier-Stokes system in a periodic box, in $\dot H^\alpha$ spaces, with $\alpha\in\big[{1/2},1\big]$. A special attention is paid to obtaining quantitative results, i.e. ones with explicit or at least computable constants, and to scaling.