Asymptotic stability of Landau solutions to Navier-Stokes system

TL;DR

This paper proves that a family of explicit, axisymmetric stationary solutions to the 3D Navier-Stokes equations are asymptotically stable under any L^2 perturbation, enhancing understanding of fluid stability.

Contribution

It demonstrates the asymptotic stability of Landau solutions to the Navier-Stokes system for the first time under general L^2 perturbations.

Findings

Landau solutions are asymptotically stable in L^2 norm.

Stability holds for all perturbations in the L^2 space.

Provides new insights into the long-term behavior of specific Navier-Stokes solutions.

Abstract

It is known that the three dimensional Navier-Stokes system for an incompressible fluid in the whole space has a one parameter family of explicit stationary solutions, which are axisymmetric and homogeneous of degree -1. We show that these solutions are asymptotically stable under any $L^2$-perturbation.