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Regularization of Navier–Stokes and Generalized Poincaré–Hopf Theorem under the NMSI–π–γ_diss–e Framework: & Dynamic Zero Concept

Author:

Lazarev, Sergiu Vasili

Category:

Research Papers

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

October 2, 2025

File:

/Research Papers-Mathematics and Applied Mathematics/Download/10327

Downloads:

122

Keywords:

Navier–Stokes Regularity; Millennium Problem; NMSI; Dynamic Zero; Oscillatory Forcing; Exponential Operator; Turbulence Modeling; Hypersonic Flows; Generalized Poincaré–Hopf Theorem; Fluid Dynamics; Subquantum Oscillations

Abstract:

This paper consolidates two augmented approaches to the Millennium Problem of Navier–Stokes Regularity under the NMSI framework. The first variant introduced the cyclic oscillatory forcing operator (π*) and the intermittent dissipation tensor (γ_diss), ensuring global smoothness by bounding energy and enstrophy. The second variant extended this framework with the exponential stabilization operator (e), providing a mathematically rigorous mechanism for exponential damping of instabilities and enabling broader applicability to atmospheric, hypersonic, and astrophysical turbulence. Additionally, we generalize the Poincaré–Hopf theorem by introducing the novel concept of dynamic zero, which reframes singularities not as static breakdowns but as transient oscillatory nodes, dynamically redistributed in phase space. This unifies recent results on unstable singularities (e.g., PINN-discovered Navier–Stokes profiles) with the NMSI-augmented framework, offering a coherent interpretation across mathematics, physics, and cosmology. The paper presents analytical derivations, numerical benchmarks (Taylor–Green vortices, hypersonic blunt-body flows), and comparative RMSE validation against experimental data. Results show consistent stabilization and boundedness, with RMSE reductions of 30–47% in hypersonic test cases. .../...

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