On the global well-posedness of 3-D axi-symmetric Navier-Stokes system with small swirl component

2017/02/21 by Y. Liu, Yanlin Liu, Ping Zhang +2 · 2 citations
Engineering · Mathematics · #35Q30 #76D03 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Component (thermodynamics) #Computer science #FOS: Mathematics #Lebesgue integration #Mathematical analysis #Mathematics #Navier-Stokes equation solutions #Physics #Small data #Stability and Controllability of Differential Equations #math.AP #msc:35Q30 #msc:76D03

paper · pdf · doi:10.48550/arxiv.1702.06279

published in arXiv (Cornell University) (Cornell University)

arxiv created 2017/02/21 · openalex publication_date 2017/02/21 · arxiv updated 2017/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper, we prove the local well-posedness of 3-D axi-symmetric Navier-Stokes system with initial data in the critical Lebesgue spaces. We also obtain the global well-posedness result with small initial data. Furthermore, with the initial swirl component of the velocity being sufficiently small in the almost critical spaces, we can still prove the global well-posedness of the system.

Citations

• 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

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