Stability of a class of exact solutions of the incompressible Euler equation in a disk

2024/08/28 by Guodong Wang, Wang, Guodong · 3 citations
Earth and Planetary Sciences · Mathematics · #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2408.15598

openalex publication_date 2024/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a sharp orbital stability result for a class of exact steady solutions, expressed in terms of Bessel functions of the first kind, of the two-dimensional incompressible Euler equation in a disk. A special case of these solutions is the truncated Lamb dipole, whose stream function corresponds to the second eigenfunction of the Dirichlet Laplacian. The proof is achieved by establishing a suitable variational characterization for these solutions via conserved quantities of the Euler equation and employing a compactness argument.

Cited by

• Quantitative stability of a class of explicit steady Euler flows in a disk
• Stability of Lamb dipoles for odd-symmetric and non-negative initial disturbances without the finite mass condition
• On the positive constant in Arnold's second stability theorem for a bounded domain

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