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Dynamic Stability of the 3D Axi-symmetric Navier-Stokes Equations with Swirl
| Content Provider | CiteSeerX |
|---|---|
| Author | Hou, Thomas Y. Li, Congming |
| Abstract | 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. |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Dynamic Stability Axi-symmetric Navier-stokes Equation Navier-stokes Equation Initial Data Nonlinear Structure Global Smooth Solution Finite Time Interesting Property Surprising Dynamic Depletion Mechanism Symmetry Axis Axisymmetric Navier-stokes Equation Short Time Exact Solution Global Regularity Special Nonlinear Structure Important Property Tremendous Dynamic Growth Large Dynamic Growth |
| Content Type | Text |
