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Solving the Millennium Problem, Navier-Stokes Regularity Under the Poincaré-Perelman_NMSI_π*-HDQG Framework

Author:

Lazarev, Sergiu Vasili

Category:

Research Papers

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

September 25, 2025

File:

/Research Papers-Mathematics and Applied Mathematics/Download/10318

Downloads:

579

Keywords:

Navier–Stokes existence and smoothness; Millennium Prize Problem; oscillatory interference; Poincaré–Perelman geometry; NMSI (New Subquantum Informational Mechanics); π* operator; HDQG (Hyper-Dissipative Quantum Gravity); turbulenc

Abstract:

We present an augmented framework addressing the Millennium Prize Problem on the existence and smoothness of the Navier–Stokes equations. Instead of treating the classical system in isolation, we embed fluid dynamics within the Poincaré–Perelman_NMSI_π*–HDQG formalism, where subquantum oscillatory physics introduces a bounded cyclic forcing term (π*) and a dissipative tensor (γ_diss). Within this extended setting, we prove that global solutions exist and remain smooth for all , as oscillatory interference and dissipative channels preclude finite-time blow-up. Thus, while we do not claim a resolution of the Clay problem in its strict mathematical formulation, we demonstrate that singularities are excluded once physically required terms are incorporated. Our approach is testable and falsifiable: it yields quantitative predictions connecting microscopic oscillatory dynamics to macroscopic turbulence and cosmological observables. This establishes a physically motivated pathway toward singularity avoidance, unifying micro- and macro-scale fluid dynamics under the NMSI–π*–HDQG framework.

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