The Aubry set for a version of the Vlasov equation
Ugo Bessi
TL;DR
This paper extends key properties of the Aubry set, originally established for finite-dimensional Lagrangians, to the infinite-dimensional setting of the Vlasov equation on the circle, involving many interacting particles.
Contribution
It demonstrates that properties of the Aubry set hold for the Vlasov equation, bridging finite and infinite-dimensional dynamical systems.
Findings
Properties of the Aubry set are preserved in the Vlasov equation setting.
The work generalizes finite-dimensional results to an infinite-dimensional context.
Supports the applicability of Aubry-Mather theory to kinetic equations.
Abstract
We check that several properties of the Aubry set, first proven for finite-dimensional Lagrangians by Mather and Fathi, continue to hold in the case of the infinitely many interacting particles of the Vlasov equation on the circle.
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Taxonomy
TopicsGas Dynamics and Kinetic Theory · Advanced Thermodynamics and Statistical Mechanics · Markov Chains and Monte Carlo Methods