Helicity is the only invariant of incompressible flows whose derivative is continuous in the \(C^1\) topology

DOI10.1134/S0001434616030366zbMath1422.58001arXiv1511.03746OpenAlexW2267395770MaRDI QIDQ325679

E. A. Kudryavtseva

Publication date: 18 October 2016

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.03746

zbMATH Keywords

fluxincompressible flowhelicityexact divergence-free vector fieldtopological invariants of magnetic fields

Mathematics Subject Classification ID

General theory of rotating fluids (76U05) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Differentiable maps on manifolds (58C25) Differential invariants (local theory), geometric objects (53A55)

Related Items (7)

The Godbillon–Vey invariant as a restricted Casimir of three-dimensional ideal fluids* ⋮ The trunkenness of a volume-preserving vector field ⋮ Continuous orbital invariants of integrable Hamiltonian systems ⋮ The Godbillon-Vey invariant as topological vorticity compression and obstruction to steady flow in ideal fluids ⋮ The Biot-Savart operator of a bounded domain ⋮ Asymptotic invariants of 3-dimensional vector fields ⋮ The helicity uniqueness conjecture in 3d hydrodynamics

Cites Work

• A generic incompressible flow is topological mixing
• Sur la structure du groupe des difféomorphismes qui preservent une forme symplectique
• Recurrence and genericity
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