L²-asymptotic stability of mild solutions to Navier-Stokes system in R³

2013/08/30 by Grzegorz Karch, Dominika Pilarczyk, Karch, Grzegorz +4
Engineering · Mathematics · #35B40 #35Q30 #76D05 #76D07 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP #msc:35B40 #msc:35Q30 #msc:76D05 #msc:76D07

paper · pdf · doi:10.48550/arxiv.1308.6667

26 pages

arxiv created 2013/08/30 · openalex publication_date 2013/08/30 · arxiv updated 2013/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider global-in-time small mild solutions of the initial value problem to the incompressible Navier-Stokes equations in R³. For such solutions, an asymptotic stability is established under arbitrarily large initial L²-perturbations.

Citations

• On blow-up "twistors" for the Navier--Stokes equations in R³: a view from reaction-diffusion theory
• StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions
• Sur le mouvement d'un liquide visqueux emplissant l'espace

Related

• On L^3,∞-stability of the Navier-Stokes system in exterior domains
• Stability of 2D incompressible flows in \bf R³
• Existence of local suitable weak solutions to the Navier-Stokes equations for initial data in L²_{\rm loc} (ℝ³)
• Asymptotic stability of homogeneous solutions to Navier-Stokes equations under L^p-perturbations
• Wellposedness and stability results for the Navier-Stokes equations in \mathbf R³