Shows that acoustic boundary conditions bottleneck turbulent energy cascade in 3D fluid flow, highlighting implications for solution existence.
The existence of global smooth solutions to the 3D Navier-Stokes equations remains a Millennium Prize Problem. We employ the Ouroboros Framework to demonstrate that when the fluid domain is constrained by modulo-9 acoustic resonance boundary conditions, the turbulent energy cascade is systematically bottlenecked.Formal Verification & Source Code: The rigorous Lean 4 proofs and framework codebase are open-source and available at the Ouroboros GitHub Repository.
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Bruno Luçardo Olivaes (2026) studied this question.
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