A card from a free library — ask anything, no account, works offline. Every card carries its source.
Euler flow is geodesic flow on the volume-preserving diffeomorphisms
joint
Arnold (1966): the Euler equations of an ideal fluid are the geodesic equations of the group of volume-preserving diffeomorphisms with the kinetic-energy metric - the fluid as a point moving on an infinite-dimensional manifold, the same geometric analysis Perelman's proof lives in. It has not produced regularity for Navier-Stokes; the join is real and the question stays open.
source
Narrow Highway - the Millennium floor, a joint found in the literature (operator seed)
card id
card_joint_arnold_geodesics
address
WIT.codex.EXP/euler-flow-is-geodesic-flow-on-the-volume-preser/REF.WITNESSED@narrow-highway-the-mille
adjoining cards
- part of → The Millennium floor - seven open questions, and where they connect — a joint that is proven or observed - a part of the floor
- connects at → Navier-Stokes existence and smoothness — Euler flow is geodesic flow on the volume-preserving diffeomorphisms. arnold 1966. Cited,
- connects at → The Poincare conjecture — Euler flow is geodesic flow on the volume-preserving diffeomorphisms. arnold 1966. Cited,
- cites → V. I. Arnold 1966 — Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits — the record the joint stands on
Is this card incomplete? Tell the library — it will call out for more ↗