Recursive Collapse Scaffold Resolving the Navier–Stokes Global Regularity Problem
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2025
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| _version_ | 1866901840936828928 |
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| author | Pryately, Carney Shea |
| author_facet | Pryately, Carney Shea |
| contents | <p>This work introduces the Recursive Collapse Scaffold Function Ψ(x,t), a novel recursive energy stabilizer that guarantees global regularity for the 3D incompressible Navier–Stokes equations. Ψ(x,t) encodes local enstrophy and bounded time recursion, detecting collapse motifs (Flat Loop) and triggering symbolic recovery (Spiral Recursion). The proof shows that Ψ is bounded and differentiable, allowing the reconstruction of a smooth velocity field u(x,t) for all time. Collapse is reframed as a recursive failure of memory, and Ψ provides its structural resolution. This result resolves the Clay Millennium Problem of smoothness and existence in the Navier–Stokes equations.</p> <p><strong>Commercial use of this code, method, or results requires written permission.</strong><br>For licensing, partnership, or commercial inquiries, please contact the author directly: </p> <p>Email: carney.shea@outlook.com</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15651300 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Recursive Collapse Scaffold Resolving the Navier–Stokes Global Regularity Problem Pryately, Carney Shea navier-stokes recursive collapse flat loop spiral recovery enstrophy smoothness turbulence PDE nonlinear systems memory regulation global regularity <p>This work introduces the Recursive Collapse Scaffold Function Ψ(x,t), a novel recursive energy stabilizer that guarantees global regularity for the 3D incompressible Navier–Stokes equations. Ψ(x,t) encodes local enstrophy and bounded time recursion, detecting collapse motifs (Flat Loop) and triggering symbolic recovery (Spiral Recursion). The proof shows that Ψ is bounded and differentiable, allowing the reconstruction of a smooth velocity field u(x,t) for all time. Collapse is reframed as a recursive failure of memory, and Ψ provides its structural resolution. This result resolves the Clay Millennium Problem of smoothness and existence in the Navier–Stokes equations.</p> <p><strong>Commercial use of this code, method, or results requires written permission.</strong><br>For licensing, partnership, or commercial inquiries, please contact the author directly: </p> <p>Email: carney.shea@outlook.com</p> |
| title | Recursive Collapse Scaffold Resolving the Navier–Stokes Global Regularity Problem |
| topic | navier-stokes recursive collapse flat loop spiral recovery enstrophy smoothness turbulence PDE nonlinear systems memory regulation global regularity |
| url | https://doi.org/10.5281/zenodo.15651300 |