Abstract
Statistical equilibrium states for a linear transport equation were defined in a previous work. We consider here the two-dimensional case: we show that under some mild assumptions these equilibrium states actually describe the long-time dynamics of the system.
References
M. Jirina, On regular conditional probabilities,Czech. Math. J. 9(3):445 (1959).
J. Michel and R. Robert, Large deviations for Young measures and statistical mechanics of infinite dimensional dynamical systems with conservation law,Commun. Math. Phys. 159:195–215 (1994).
J. Michel, Thesis, Université Lyon 1 (1993).
S. R. S. Varadhan, Large deviations and applications, Ecole d'été de probabilité de Saint-Flour XV–XVII, 1985–1987.
L. C. Young, Generalized surfaces in the calculus of variations,Ann. Math. 43:84–103 (1942).
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Communicated by J. L. Lebowitz
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Michel, J., Robert, R. Statistical equilibrium states and long-time dynamics for a transport equation. J Stat Phys 83, 779–789 (1996). https://doi.org/10.1007/BF02183750
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DOI: https://doi.org/10.1007/BF02183750