Author: Giovanni Gallavotti, Lamberto Rondoni, Enrico Segre

Title: Lyapunov spectra and nonequilibrium ensembles equivalence in 2D fluid mechanics

Abstract: Abstract. 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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Giovanni Gallavotti
Fisica, Universita' di Roma 1
P.le Moro 2
00185 Roma, Italia
tel +39-06-4991-4370
fax +39-06-4957697

em: giovanni.gallavotti@roma1.infn.it
http://ipparco.roma1.infn.it

Lamberto Rondoni, Enrico Segre
Politecnico di Torino
Corso Duca degli Abruzzi
Torino, Italia
em: rondoni@polito.it, segre@polito.it