科研之友
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摘要
Stability analysis of the rotating B,nard problem gives a spectral instability threshold of the purely conducting solution that can be expressed as a critical Rayleigh number R (2) depending on the Taylor number T (2). The definition of a functional which can be used to prove Lyapunov stability up to the threshold of spectral instability (optimal Lyapunov function) is an important step forward both, for a proof of nonlinear stability and for the investigation of the basin of attraction of the equilibrium. %26lt;br%26gt;In previous works a Lyapunov function was found, but its optimality could be proven only for small T (2). In this work we describe the reason why this happens, and provide a weaker definition of Lyapunov function which allows to prove that, for the linearized system, the spectral instability threshold is also the Lyapunov stability threshold for every value of T (2).
- 出版日期2014-8
