Asymptotic stability for the 3D Navier-Stokes equations in L³ and nearby spaces

2024/09/19 by Zachary Bradshaw, Weinan Wang, Bradshaw, Zachary +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2409.12918

openalex publication_date 2024/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a short proof of L³-asymptotic stability around vector fields that are small in weak-L³, including small Landau solutions. We show that asymptotic stability also holds for vector fields in the range of Lorentz spaces strictly between L³ and weak-L³, as well as in the closure of the test functions in weak-L³. To provide a comprehensive perspective on the matter, we observe that asymptotic stability of Landau solutions does not generally extend to weak-L³ via a counterexample.

Cited by

• Recent research on (-1)-homogeneous solutions of stationary Navier-Stokes equations

Related

• Asymptotic stability of Landau solutions to Navier-Stokes system under L^p-perturbations
• Asymptotic stability of homogeneous solutions to Navier-Stokes equations under L^p-perturbations
• L²-asymptotic stability of mild solutions to Navier-Stokes system in R³
• Asymptotics of small exterior Navier-Stokes flows with non-decaying boundary data
• On L^3,∞-stability of the Navier-Stokes system in exterior domains