Euler evolution of a concentrated vortex in planar bounded domains

2018/01/05 by Daomin Cao, Guodong Wang, Cao, Daomin +1
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics #math.AP

paper · pdf · doi:10.48550/arxiv.1801.01629

15 pages

arxiv created 2018/01/05 · openalex publication_date 2018/01/05 · arxiv updated 2018/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the time evolution of an ideal fluid in a planar bounded domain. We prove that if the initial vorticity is supported in a sufficiently small region with diameter ε, then the time evolved vorticity is also supported in a small region with diameter d, d≤ Cε^α for any α<(1)/(3), and the center of the vorticity tends to the point vortex, the motion of which is described by the Kirchhoff-Routh equation.

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