Dynamic Stability of the 3D Axi-symmetric Navier-Stokes Equations with Swirl
| dc.creator | Hou, Thomas Y. | |
| dc.creator | Li, Congming | |
| dc.date | 2006-08-12 | |
| dc.date.accessioned | 2026-07-07T07:21:41Z | |
| dc.date.available | 2026-07-07T07:21:41Z | |
| dc.description | In this paper, we study the dynamic stability of the 3D axisymmetric Navier-Stokes Equations with swirl. To this purpose, we propose a new one-dimensional (1D) model which approximates the Navier-Stokes equations along the symmetry axis. An important property of this 1D model is that one can construct from its solutions a family of exact solutions of the 3D Navier-Stokes equations. The nonlinear structure of the 1D model has some very interesting properties. On one hand, it can lead to tremendous dynamic growth of the solution within a short time. On the other hand, it has a surprising dynamic depletion mechanism that prevents the solution from blowing up in finite time. By exploiting this special nonlinear structure, we prove the global regularity of the 3D Navier-Stokes equations for a family of initial data, whose solutions can lead to large dynamic growth, but yet have global smooth solutions. | |
| dc.identifier | https://arxiv.org/abs/math/0608295 | |
| dc.identifier | http://arxiv.org/abs/math/0608295 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115386 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Dynamic Stability of the 3D Axi-symmetric Navier-Stokes Equations with Swirl | |
| dc.type | text |