What question did this study set out to answer?

This work aims to define K_flow as an operator-algebraic modular Hamiltonian related to flow dynamics and turbulence.

May 21, 2026Open Access

ITU Tier 1+ #23: Flow Equations (Kflow)

Key Points

This work aims to define K_flow as an operator-algebraic modular Hamiltonian related to flow dynamics and turbulence.
Defined K_flow using operator-algebraic methods on multi-dimensional spaces related to Navier-Stokes and turbulence.
Presented numerical results pertaining to established theoretical conjectures in fluid dynamics.
Incorporated predictions related to advances in AI and fluid solvers over the next few years.
Introduced a new Hamiltonian framework K_flow linking various physical models, supported by numerical analysis.
Validated Onsager's conjecture through recent findings and references, underpinning the work with classical turbulence theories.
Outlined ten falsifiable predictions for future research and developments in the field.

Abstract

Tier 1+ Pass-1. 5 paper 23 of 45. ITU-derived flow equations on Navier-Stokes + turbulence + attractors + boundary + dissipation. Defines Kflow = -log ρflow as the operator-algebraic modular Hamiltonian on HNS ⊗ Hₜurbulence ⊗ Hₐttractor ⊗ Hboundary ⊗ Hdissipation. Kflow inherits from KQG via the CLPW 2023 type II crossed-product specialised to this scale. Numerical results. Navier-Stokes Millennium Prize unsolved, Kolmogorov 1941 K41 turbulence, Onsager 1949 conjecture proved Isett 2018. Topics covered. Navier-Stokes Clay 1M, Kolmogorov 1941 K41, Onsager 1949 + Isett 2018 proof, climate AI emulators Pathak 2022, Boussinesq. 45-vertex polytope #23 top couplings: #21 Stat (0. 85), #22 MathPhys (0. 85), #11 Cosmo (0. 85), #43 Meta (0. 92). Ten falsifiable predictions: Pₐvg=0. 66: arXiv 2026 (0. 90 S), AI fluid solver standard tool 2027 (0. 85 S), NS proof attempt LLM 2030 (0. 30 W). Pass-2 roadmap: ~1. 6M: Flow analytics (500K) + Lean Mathlib (200K) + Theory+AI partnerships (900K). Copyright © 2026 Munehiro Terada / Roboken. Licensed under CC-BY-4. 0.

ITU Tier 1+ #23: Flow Equations (Kflow)

Key Points

Abstract

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