Friedlander Susan, Vishik Misha M.
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60680Department of Mathematics, University of Texas, Austin, Texas 78712.
Chaos. 1992 Jul;2(3):455-460. doi: 10.1063/1.165888.
An instability criterion based on the positivity of a Lyapunov-type exponent is used to study the stability of the Euler equations governing the motion of an inviscid incompressible fluid. It is proved that any flow with exponential stretching of the fluid particles is unstable. In the case of an arbitrary axisymmetric steady integrable flow, a sufficient condition for instability is exhibited in terms of the curvature and the geodesic torsion of a stream line and the helicity of the flow.
基于李雅普诺夫型指数的正性的一个不稳定性判据被用于研究控制无粘性不可压缩流体运动的欧拉方程的稳定性。证明了任何具有流体粒子指数拉伸的流动都是不稳定的。在任意轴对称定常可积流动的情况下，根据流线的曲率和测地挠率以及流动的螺旋度给出了一个不稳定性的充分条件。
