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Theoretical study reveals geometric constraints for vorticity direction in 3D incompressible Navier–Stokes flows, highlighting flawed continuity claims.
This note is the geometric ledger for vorticity direction of unmodified 3D incompressible Navier–Stokes on the maximal classical interval [0, T*). What it proves. The implication Definition 7.1 ⇒ T*=∞ as Constantin–Fefferman / Beirão da Veiga–Berselli (not a new regularity theorem). The direction equation on {r>0}, with Pξ and ν|∇ξ|²ξ. S ∈ L²_t L²_x from energy and Calderón–Zygmund on L², without ‖ω‖_∞. The claims drift = O(1/Ω) and De Giorgi–Nash–Moser ⇒ uniform C0,1/2 of ξ on E(t) are false. Pairings are named as the real identities: stretching is a real cubic in ω; Arnold is real alternating bilinear; B(F,G) is real symmetric bilinear; S is a real symmetric tensor; ξ is a real unit vector field, S²-valued. This is not a Clay solution. Distinct from Zenodo 22153742 (Ω₀ lattice note).
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Benjamin Stanley Frohman (2026) studied this question.
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