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Stability of degree-2 Rossby-Haurwitz waves

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arxiv 2305.03279 v3 pith:B6CSCDZO submitted 2023-05-05 math.AP

Daomin Cao , Guodong Wang , Bijun Zuo This is my paper · ORCID
classification math.AP
keywords wavesstabilityapproachdegree-2flowsrossby-haurwitzsolutionsvariational
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Rossby-Haurwitz (RH) waves are important explicit solutions of the incompressible Euler equation on a two-dimensional rotating sphere. In this paper, we prove the orbital stability of degree-2 RH waves, which confirms a conjecture proposed by A. Constantin and P. Germain in [Arch. Ration. Mech. Anal. 245, 587-644, 2022]. The proofs are based on a variational approach, with the main challenge being to establish suitable variational characterizations for the solutions under consideration. In this process, the set of rearrangements of a fixed function plays a vital role. We also apply our approach to the stability analysis of degree-1 RH waves, Arnold-type flows, and zonal flows with monotone absolute vorticity.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Orbital Stability of First Laplacian Eigenstates for the Incompressible Euler Equation on a Flat 2-Torus

    math.AP 2025-08 accept novelty 6.0 of 10

    First Laplacian eigenstates on flat 2-tori of any shape are orbitally stable for 2D Euler dynamics up to translations, including new stable sinusoidal flows on hexagonal tori.

  2. Regularization for point vortices on $\mathbb S^2$

    math.AP 2024-11 conditional novelty 6.0 of 10

    The authors construct small vortex patch solutions on the rotating sphere that converge to von Kármán vortex streets and general point vortex equilibria.

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