Dynamic stability of the three-dimensional axisymmetric Navier-Stokes equations with swirl
Dynamic stability of the three-dimensional axisymmetric Navier-Stokes equations with swirl
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DOI：
10.1002/cpa.20212
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发表时间：
2008-05-01
影响因子：
3
通讯作者：
Ll, Congming
中科院分区：
文献类型：
--
作者：
Hou, Thomas Y.;Ll, Congming
本文研究了三维轴对称Navier-Stokes方程组的动力稳定性。为此，我们提出了一个新的一维模型，近似的Navier-Stokes方程沿着对称轴。这个一维模型的一个重要性质是可以从它的解构造出三维Final Navier-Stokes方程的一族精确解。一维模型的非线性结构具有一些非常有趣的性质。一方面，它可以在短时间内导致解决方案的巨大动态增长。另一方面，它有一个令人惊讶的动态耗尽机制，可以防止溶液在有限时间内爆炸。通过利用这种特殊的非线性结构，我们证明了三维Navier-Stokes方程的全局正则性的一个家庭的初始数据，其解决方案可以导致大的动态增长，但仍然有全球光滑的解决方案。(C)2007 Wiley Periodicals，Inc.
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 three-dimensionalFinal Navier-Stokes equations. The nonlinear structure of the one-dimensional 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.