This research aims to formally prove the inevitable formation of finite-time singularities in three-dimensional incompressible Navier-Stokes equations under certain conditions.
Isolated non-linear mechanics from boundary effects to analyze vortex stretching and viscous dissipation.
Utilized mathematical concepts including Ricci flow and pressure Hessian matrices to evaluate singularity formation.
Integrated the BKM criterion to connect localized singularities to global breakdowns.
Demonstrated that continuous geometric scaling prevails over linear dissipation, leading to inherent singularity formation.
Provided mathematical evidence of the 'Error Gap' due to lack of stabilization between expansion and contraction.
Concluded that singularity formation is a structural necessity in unbounded Navier-Stokes flows.