二维流体力学中的李雅普诺夫谱与非平衡系综等价性
Lyapunov spectra and nonequilibrium ensembles equivalence in 2D fluid mechanics
摘要：
我们进行数值实验，研究与Navier-Stokes（NS）方程在两个空间维截断的傅立叶基动力系统的李雅普诺夫谱。近年来，人们提出了一种新的方程，称为GNS方程，并证明在大雷诺数下它与NS方程是等价的。的NS和相应的GNS系统的李雅普诺夫谱重叠，增加了证据，有利于已研究和部分扩展在以前的论文中的约束等价。我们利用李雅普诺夫谱来研究一个波动关系，它被提出来将“波动定理”扩展到强耗散系统。对制定的波动公式的本地版本的初步结果也提出。
英文摘要：
We perform numerical experiments to study the Lyapunov spectra of dynamical systems associated with the Navier--Stokes (NS) equation in two spatial dimensions truncated over the Fourier basis. Recently new equations, called GNS equations, have been introduced and conjectured to be equivalent to the NS equations at large Reynolds numbers. The Lyapunov spectra of the NS and of the corresponding GNS systems overlap, adding evidence in favor of the conjectured equivalence already studied and partially extended in previous papers. We make use of the Lyapunov spectra to study a fluctuation relation which had been proposed to extend the ``fluctuation theorem'' to strongly dissipative systems. Preliminary results towards the formulation of a local version of the fluctuation formula are also presented.
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