Long time confinement of multiple concentrated vortices

2025/06/02 by Meyer, David
Earth and Planetary Sciences · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing

paper · pdf · doi:10.48550/arxiv.2506.01477

openalex publication_date 2025/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

We study the stability of multiple almost circular concentrated vortices in a fluid evolving according to the two-dimensional Euler equations. We show that, for general configurations, they must remain concentrated on time-scales much longer than previously known as long as they remain separated. We further prove a new stability estimate for the logarithmic interaction energy as part of the proof.

Citations

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Related

• Long-time Confinement near Special Vortex Crystals
• Two-Point Vortex Confinement in a simply connected domain
• Stability of two-dimensional steady Euler flows with concentrated vorticity
• Construction of unstable concentrated solutions of the Euler and gSQG equations
• Stability of vortex quadrupoles with odd-odd symmetry