Quantitative stability of the Rossby--Haurwitz waves of degree two for the Euler equation on S²

Q: What type of study is this?

This is a Quantitative Study study.

Matías G. Delgadino; Luca Melzi

doi:10.48550/arxiv.2509.16156

September 19, 2025Open Access

Quantitative stability of the Rossby--Haurwitz waves of degree two for the Euler equation on S²

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Key Points

The degree-2 Rossby–Haurwitz waves are shown to be orbitally stable under the Euler equation on $ ext{S}^2$.
The proof provided is concise, quantitative, and easy to follow, ensuring clarity in understanding stability.
This analysis has implications for studying wave patterns in fluid dynamics, particularly on spherical surfaces.
The results may contribute to broader applications in meteorology and oceanography by establishing foundational stability.

Implication

This analysis shows orbital stability of degree-2 Rossby–Haurwitz waves on $ ext{S}^2$, indicating their robustness under perturbations.

Abstract

We show that the degree-2 Rossby--Haurwitz travelling waves on the Euler equation on S² are orbitally stable. Our proof is short, quantitative, and conceptually easy to follow.

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Cite This Study

Delgadino et al. (2025) studied this question.

synapsesocial.com/papers/68e040eda99c246f578b3514 https://doi.org/10.48550/arxiv.2509.16156

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Quantitative stability of the Rossby--Haurwitz waves of degree two for the Euler equation on S²

Key Points

Implication

Abstract

Discussion

Cite This Study

Quantitative stability of the Rossby--Haurwitz waves of degree two for the Euler equation on S²

Key Points

Implication

Abstract

Discussion

Cite This Study

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