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

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.

35 pages

References in corpus (2)

• On the global wellposedness of the 3-D Navier-Stokes equations with large initial data
• On the regularity set and angular integrability for the Navier--Stokes equation