Guardat en:
| Autor principal: | |
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| Format: | Recurso digital |
| Idioma: | anglès |
| Publicat: |
Zenodo
2026
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| Matèries: | |
| Accés en línia: | https://doi.org/10.5281/zenodo.19324392 |
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- <div> <div>We introduce the Helical Sobolev space H^s_B, a state-dependent Finsler manifold embedding the Beltrami alignment angle theta(x,t) between velocity and vorticity directly into the metric of the critical fractional Sobolev space H-dot^{1/2}. Within this framework, the Kato–Ponce trilinear bound becomes state-dependent with effective constant C_eff proportional to sin theta, and the Groenwall inequality closes globally provided ||sin theta||_{L^infty} <= nu/C_0. This conditional regularity result provides the first unified bridge between the geometric criterion of Constantin–Fefferman (1993) and the critical-space theorem of Escauriaza–Seregin–Sverak (2003), reducing the 3D Navier–Stokes global regularity problem to a single geometric inequality—the Geometric Suppression Conjecture—which we state precisely and provide empirical and partial analytical support for.</div> <br> <div>The manuscript further formulates the Fundamental Lemma of Fluid Contact Geometry, records obstructions for an explicit metric candidate, and proves a no-go theorem: no local uniformly elliptic Riemannian metric can absorb pressure for all solutions in the sense stated in the paper. It does not claim resolution of the Clay Millennium Prize problem.</div> </div>