Asymptotic stability of Landau solutions to Navier-Stokes system under $L^p$-perturbations

TL;DR

This paper proves the asymptotic stability of Landau solutions to the Navier-Stokes equations under $L^3$-perturbations, establishing well-posedness and decay properties in various $L^p$ spaces.

Contribution

It provides new results on the stability, well-posedness, and decay of solutions near Landau solutions in multiple $L^p$ settings.

Findings

Landau solutions are asymptotically stable under $L^3$-perturbations.

Established local and global well-posedness in $L^3$ space.

Studied decay rates in $L^q$ spaces for $q>3$.

Abstract

In this paper, we show that Landau solutions to the Navier-Stokes system are asymptotically stable under $L^3$-perturbations. We give the local well-posedness of solutions to the perturbed system with initial data in $L_{\sigma}^3$ space and the global well-posedness with small initial data in $L_{\sigma}^3$ space, together with a study of the $L^q$ decay for all $q>3.$ Moreover, we have also studied the local well-posedness, global well-posedness and stability in $L^p$ spaces for $3<p<\infty$.