Global existence of weak solutions to the 3D incompressible axisymmetric Euler equations without swirl

2016/05/22 by Quansen Jiu, Jitao Liu, Jiu, Quansen +3
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1605.06740

openalex publication_date 2016/05/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we mainly investigate the tridimensional incompressible axisymmetric Euler equations without swirl in the whole space. Specifically, we prove the global existence of weak solutions if the swirl component of initial vorticity w₀^θ satisfies that \fracw₀^θr∈ L¹∩ L^p(\Bbb R³) for some p>1. To achieve this goal, we establish the L_{\rm loc}^2+α(\Bbb R³) estimate of velocity fields for some α>0, which is innovative to the best of our knowledge. Our result extends previous work in the literature.

Citations

• Global existence of weak solutions to the three-dimensional Euler equations with helical symmetry

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