Stability of radially symmetric, monotone vorticities of 2D Euler equations

2021/03/22 by Kyudong Choi, Choi, Kyudong, Deokwoo Lim +1 · 3 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #35Q35 #76B47 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Stochastic processes and financial applications #math-ph #math.AP #math.MP #msc:35Q35 #msc:76B47

paper · pdf · doi:10.48550/arxiv.2103.11724

29 pages

arxiv created 2021/03/22 · openalex publication_date 2021/03/22 · arxiv updated 2021/03/23 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We consider the incompressible Euler equations in R² when the initial vorticity is bounded, radially symmetric and non-increasing in the radial direction. Such a radial distribution is stationary, and we show that the monotonicity produces stability in some weighted norm related to the angular impulse. For instance, it covers the cases of circular vortex patches and Gaussian distributions. Our stability does not depend on L^∞-bound or support size of perturbations. The proof is based on the fact that such a radial monotone distribution minimizes the impulse of functions having the same level set measure.

Cited by

• Vortex atmospheres of traveling vortices: rigorous definition, existence, and topological classification
• Time-periodic non-radial solutions near monotone vortices in linearized 2D Euler
• Long time confinement of multiple concentrated vortices

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