Asymptotic stability of homogeneous solutions to Navier-Stokes equations under L^p-perturbations

2023/04/03 by Zhao, Zhiwen, Xiaoxin Zheng, Zheng, Xiaoxin · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2304.00840

openalex publication_date 2023/04/03 · openalex created_date 2023/04/07 · openalex updated_date 2026/07/28

Abstract

It is known that there has been classified for all (-1)-homogeneous axisymmetric no-swirl solutions of the three-dimensional Navier-Stokes equations with a possible singular ray. The main purpose of this paper is to show that the least singular solutions among such solutions other than Landau solutions to the Navier-Stokes equations are asymptotically stable under L³-perturbations. Moreover, we establish the L^q decay estimate with an explicit decay rate and a sharp constant for any q>3. For that purpose, we first study the global well-posedness of solutions to the perturbed equations under small initial data in L_σ³ space and the local well-posedness with any initial data in L_σ^p spaces for p≥3.

Cited by

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

Related

• Asymptotic stability of homogeneous solutions of incompressible stationary Navier-Stokes equations
• Asymptotic stability of Landau solutions to Navier-Stokes system under L^p-perturbations
• Asymptotic stability for the 3D Navier-Stokes equations in L³ and nearby spaces
• L²-asymptotic stability of mild solutions to Navier-Stokes system in R³
• Stability of singular solutions to the Navier-Stokes system