Endogenous Momentum Focusing and the Spontaneous Loss of Regularity in 3D Navier-Stokes Flows
Year: 2026
Type: preprint
Abstract: This paper establishes the spontaneous loss of global regularity in the 3D incompressible Navier-Stokes equations within a bounded cylindrical domain \Omega under zero external forcing (\mathbf{f}=0). By constructing an analytic expansion in the viscosity parameter \eta over a class of stationary Euler flows that satisfy the no-slip condition \mathbf{v}|_{\partial\Omega}=0, we identify an endogenous mechanism of axial momentum focusing. We demonstrate that the recursive coupling between viscous diffusion and non-linear advection generates a sequence of corrections whose axial gradients at the symmetry axis r=0 grow factorially. This leads to a Riccati-type divergence where the radius of convergence of the temporal series vanishes at a finite time T^{*}>0. The results provide a definitive negative resolution to the Millennium Prize problem, proving that the geometric confinement and internal inertia of the fluid are sufficient to induce a finite-time blow-up.
Author: Hernandez Rosales, Manuel
Institution: Universidad Nacional Autónoma de México
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212179547
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