On Singular Vortex Patches, II: Long-time dynamics

2019/09/30 by Tarek M. Elgindi, Elgindi, Tarek M., In‐Jee Jeong +1 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1909.13555

openalex publication_date 2019/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a companion paper, we gave a detailed account of the well-posedness theory for singular vortex patches. Here, we discuss the long-time dynamics of some of the classes of vortex patches we showed to be globally well-posed in the companion work. In particular, we give examples of time-periodic behavior, cusp formation in infinite time at an exponential rate, and spiral formation in infinite time.

Citations

• Finite-time Singularity Formation for Strong Solutions to the Boussinesq System
• Symmetry in stationary and uniformly-rotating solutions of active scalar equations

Cited by

• Desingularization of nondegenerate rotating vortex patches
• On Singular Vortex Patches, I: Well-posedness Issues

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