论文标题
Arnold在多重连接域中的第二个稳定定理的扩展
An extension of Arnold's second stability theorem in a multiply-connected domain
论文作者
论文摘要
我们为在有界的多重连接域中二维理想流体的稳定流动的非线性稳定性提供了足够的条件，该域在1960年代概述了Arnold证明的稳定性标准。证明的最重要成分是为正在考虑的稳定流量建立一个变异表征，这是基于阿诺德提出的能量 - 卡西米尔方法以及沃兰斯基和吉尔引入的支持功能方法来实现的。然后，非线性稳定性遵循与二维EULER方程的变异表征和正确使用的紧凑性参数有关。
We give a sufficient condition for the nonlinear stability of steady flows of a two-dimensional ideal fluid in a bounded multiply-connected domain, which generalizes a stability criterion proved by Arnold in the 1960s. The most important ingredient of the proof is to establish a variational characterization for the steady flow under consideration, which is achieved based on the energy-Casimir method proposed by Arnold, and the supporting functional method introduced by Wolansky and Ghil. Nonlinear stability then follows from a compactness argument related to the variational characterization and proper use of conserved quantities of the two-dimensional Euler equations.
