A Geometrically Weighted Sobolev Framework for Navier–Stokes Regularity: The H^s_B Space, Contact Geometry Interpretation, and a No-Go Theorem for Metric Pressure Absorption
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| Formato: | Recurso digital |
| Lenguaje: | inglés |
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2026
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| _version_ | 1866901375408930816 |
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| author | Jeffers, Nicholas |
| author_facet | Jeffers, Nicholas |
| contents | <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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19324392 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Geometrically Weighted Sobolev Framework for Navier–Stokes Regularity: The H^s_B Space, Contact Geometry Interpretation, and a No-Go Theorem for Metric Pressure Absorption Jeffers, Nicholas Navier-Stokes equations Sobolev spaces vorticity alignment Beltrami flows global regularity Kato-Ponce inequality geometric depletion <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> |
| title | A Geometrically Weighted Sobolev Framework for Navier–Stokes Regularity: The H^s_B Space, Contact Geometry Interpretation, and a No-Go Theorem for Metric Pressure Absorption |
| topic | Navier-Stokes equations Sobolev spaces vorticity alignment Beltrami flows global regularity Kato-Ponce inequality geometric depletion |
| url | https://doi.org/10.5281/zenodo.19324392 |