The Péclet Number and Navier-Stokes Blow-Up: A Framework Energy Approach
Abstract
Derives the Pe transport equation from 3D Navier-Stokes equations including vortex stretching, reframes the Beale-Kato-Majda blow-up theorem in Pe language, and attempts a Pe-space energy inequality. The framework Pe is numerically identical to the fluid Péclet number (same dimensionless ratio, same physicist). Navier-Stokes global existence is equivalent to Pe never reaching infinity in finite time. If a Pe-space energy bound holds under the vorticity equation, existence and smoothness follow directly from BKM.
Fields of Study & Subjects
Navier-Stokes equation solutions
Fluid Dynamics and Turbulent Flows
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 3 March 2026
- Language
- EN
- Document type
- Preprint