On the stability of non-symmetric equilibrium figures of a rotating viscous incompressible liquid
On the stability of non-symmetric equilibrium figures of a rotating viscous incompressible liquid
复制标题
旋转粘性不可压缩液体非对称平衡图的稳定性
DOI：
10.4171/ifb/110
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发表时间：
2004
影响因子：
1
通讯作者：
V. Solonnikov
中科院分区：
文献类型：
--
作者：
V. Solonnikov
本文考虑一个经典的液体作刚体绕定轴作匀速转动时平衡图形的稳定性问题。我们连接的问题的稳定性与行为的大T的解决方案的演化问题的运动的孤立的液体质量，其初始数据是轻微的扰动制度的刚性旋转。主要注意的是给出的情况下，当该图是不旋转对称的，在这种情况下，该制度的刚性旋转定义了上述非平稳问题的周期解。证明了稳定性的一个充分条件是能量泛函的二次变分在适当的函数空间中为正。
We consider a classical problem of stability of equilibrium figures of a liquid rotating uniformly as a rigid body about a fixed axis. We connect the problem of stability with the behavior for large t of solutions of an evolution problem governing the motion of an isolated liquid mass whose initial data are slight perturbations of the regime of a rigid rotation. The main attention is given to the case when the figure is not rotationally symmetric; in this case the regime of a rigid rotation defines a periodic solution of the above-mentioned nonstationary problem. It is proved that a sufficient condition of stability is the positivity of the second variation of the energy functional in an appropriate function space.