Stability properties of the regular set for the Navier--Stokes equation

TL;DR

This paper studies the stability of the regular set in Navier-Stokes equations under small perturbations, showing that regularity persists even with large data in certain weighted spaces.

Contribution

It provides new insights into the stability of regular solutions for Navier-Stokes under perturbations in weighted spaces, extending previous results to larger data regimes.

Findings

Regular set stability under small weighted perturbations

Persistence of regularity with large data in critical spaces

Results applicable to both large and small data scenarios

Abstract

We investigate the size of the regular set for small perturbations of some classes of strong large solutions to the Navier--Stokes equation. We consider perturbations of the data which are small in suitable weighted $L^{2}$ spaces but can be arbitrarily large in any translation invariant critical Banach space. We give similar results in the small data setting.