Physical Instability and Dynamical Constraints of Axisymmetric Contracting Vortex Singularity Constructions

Declaration of originality: All core physical concepts, topological framework and reasoning are independently conceived and derived by the author. This manuscript received auxiliary support for text revision, formula typesetting and logical checking from an AI assistant, which holds no invention right of the theory. Abstract:In recent years, a number of studies have claimed to prove the existence of finite-time velocity blowup singularities for the three-dimensional incompressible Navier–Stokes (NS) equations by constructing axisymmetric smooth vortex tubes with finitely smooth external force fields. Based on five complete sets of derivations including angular momentum conservation, Rayleigh centrifugal stability, radial dynamic equilibrium, turbulent perturbation growth rate, and divergent geometric surface area, this paper systematically falsifies the physical self-consistency of such singularity constructions. The results show that such proof schemes rely on the illicit physical assumption of permanently axisymmetric smooth flow, and their core velocity profiles are inherently centrifugally unstable. Angular momentum conservation leads to cubic divergence of centrifugal force with respect to radius; sustaining continuous contraction requires infinite local force density. The growth rate of 3D secondary vortex perturbations is strictly larger than the contraction speed of the vortex tube, leading to premature flow collapse into turbulence. The contraction of vortex tubes is accompanied by diverging viscous dissipation arising from finite volume paired with infinite shear surface area. All such mathematical singularity paths cannot be achieved within real continuum fluids. These blowup solutions are merely formal mathematical solutions under artificial strong constraints and lack physical authenticity in fluid mechanics. All such NS blowup constructions are mathematically formal but physically ill-posed, and cannot count as valid Millennium Problem regularity proof.