Asymptotic stability of the stationary Navier-Stokes flows in Besov spaces

TL;DR

This paper investigates the long-term stability of stationary solutions to the Navier-Stokes equations in Besov spaces, providing key estimates for the associated semigroup to establish asymptotic stability.

Contribution

It introduces a novel critical estimate for the Laplacian semigroup with perturbation, advancing understanding of Navier-Stokes stability in Besov spaces.

Findings

Established asymptotic stability of stationary solutions in Besov spaces

Developed a critical estimate for the perturbed Laplacian semigroup

Extended stability analysis to low integrability and positive smoothness Besov spaces

Abstract

We discuss the asymptotic stability of stationary solutions to the incompressible Navier-Stokes equations on the whole space in Besov spaces with positive smoothness and low integrability. A critical estimate for the semigroup generated by the Laplacian with a perturbation is main ingredient of the argument.