Large deviations and entropy production in viscous fluid flows

Abstract : We study the motion of a particle in a random time-dependent vector field defined by the 2D Navier-Stokes system with a noise. Under suitable non-degeneracy hypotheses we prove that the empirical measures of the trajectories of the pair (velocity field, particle) satisfy the LDP with a good rate function. Moreover, we show that the law of a unique stationary solution restricted to the particle component possesses a positive smooth density with respect to the Lebesgue measure in any finite time. This allows one to define a natural concept of the entropy production, and to show that its time average is a bounded function of the trajectory. The proofs are based on a new criterion for the validity of the level-3 LDP for Markov processes and an application of a general result on the image of probability measures under smooth maps to the laws associated with the motion of the particle.
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https://hal.archives-ouvertes.fr/hal-02012709
Contributeur : Armen Shirikyan <>
Soumis le : samedi 9 février 2019 - 01:43:20
Dernière modification le : vendredi 15 février 2019 - 01:16:30

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Entropy in fluid flows.pdf
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  • HAL Id : hal-02012709, version 1

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Vojkan Jaksic, Vahagn Nersesyan, Claude-Alain Pillet, Armen Shirikyan. Large deviations and entropy production in viscous fluid flows. 2019. 〈hal-02012709〉

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