The topology of Bott integrable fluids

DOI10.3934/dcds.2022054zbMath1492.35194arXiv2006.16880OpenAlexW3039667780MaRDI QIDQ2158216

Robert Cardona

Publication date: 26 July 2022

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.16880

zbMATH Keywords

Euler equationsArnold's structure theoremMorse-Bott integralstationary Euler flows

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Euler equations (35Q31) Foliations generated by dynamical systems (37C86)

Related Items (2)

Godbillon-Vey invariants of Non-Lorentzian spacetimes and Aristotelian hydrodynamics ⋮ Bott‐integrable Reeb flows on 3‐manifolds

Cites Work

• KAM theory and the 3D Euler equation
• Knots and links in steady solutions of the Euler equation
• Morse-type theory for integrable Hamiltonian systems with tame integrals
• Topological methods in hydrodynamics
• First steps in stable Hamiltonian topology
• Eine Klasse von 3-dimensionalen Mannigfaltigkeiten. I, II
• Selected topics on the topology of ideal fluid flows
• A note on the stationary Euler equations of hydrodynamics
• Topological classification of integrable Hamiltonian systems with two degrees of freedom. List of systems of small complexity
• THE TOPOLOGY OF INTEGRAL SUBMANIFOLDS OF COMPLETELY INTEGRABLE HAMILTONIAN SYSTEMS
• Characterization of Steady Solutions to the 2D Euler Equation
• Contact topology and hydrodynamics: I. Beltrami fields and the Seifert conjecture
• A characterization of 3D steady Euler flows using commuting zero-flux homologies
• Steady Euler flows and Beltrami fields in high dimensions
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