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Dynamic Stability of the Three-Dimensional Axisymmetric Navier-Stokes Equations with Swirl
| Content Provider | Semantic Scholar |
|---|---|
| Author | Hou, Thomas Y. |
| Copyright Year | 2007 |
| Abstract | In this paper, we study the dynamic stability of the three-dimensional axisymmetric Navier-Stokes Equations with swirl. To this purpose, we propose a new one-dimensional model that approximates the Navier-Stokes equations along the symmetry axis. An important property of this one-dimensional model is that one can construct from its solutions a family of exact solutions of the threedimensionaFinal Navier-Stokes equations. The nonlinear structure of the onedimensional 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 three-dimensional Navier-Stokes equations for a family of initial data, whose solutions can lead to large dynamic growth, but yet have global smooth solutions. c 2007 Wiley Periodicals, Inc. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://users.cms.caltech.edu/~hou/papers/CPAM-Hou-Li-fulltext.pdf |
| Alternate Webpage(s) | http://www.ama.caltech.edu/~hou/papers/CPAM-Hou-Li-fulltext.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Apache Axis Depletion region Genus Axis John D. Wiley Navier–Stokes equations Nonlinear system Solutions |
| Content Type | Text |
| Resource Type | Article |
