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Communications in Mathematical Physics

, Volume 336, Issue 1, pp 131–170 | Cite as

Large Deviations and Gallavotti–Cohen Principle for Dissipative PDEs with Rough Noise

  • V. Jakšić
  • V. Nersesyan
  • C.-A. Pillet
  • A. Shirikyan
Article

Abstract

We study a class of dissipative PDEs perturbed by an unbounded kick force. Under some natural assumptions, the restrictions of solutions to integer times form a homogeneous Markov process. Assuming that the noise is rough with respect to the space variables and has a non-degenerate law, we prove that the system in question satisfies a large deviation principle (LDP) in τ-topology. Under some additional hypotheses, we establish a Gallavotti–Cohen type symmetry for the rate function of an entropy production functional and the strict positivity and finiteness of the mean entropy production rate in the stationary regime. The latter result is applicable to PDEs with strong nonlinear dissipation.

Keywords

Entropy Production Burger Equation Stokes System Large Deviation Principle Entropy Production Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • V. Jakšić
    • 1
  • V. Nersesyan
    • 2
  • C.-A. Pillet
    • 3
    • 4
  • A. Shirikyan
    • 5
  1. 1.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada
  2. 2.Laboratoire de Matématiques, UMR CNRS 8100Université de Versailles-Saint-Quentin-en-YvelinesVersaillesFrance
  3. 3.Aix Marseille UniversitéMarseilleFrance
  4. 4.Univeristé de ToulonLa GardeFrance
  5. 5.Department of MathematicsUniversity of Cergy-PontoiseCergy-PontoiseFrance

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