Hydrodynamic limit for the velocity-flip model

Marielle Simon (1)

1 PUC-Rio - Pontifícia Universidade Católica do Rio de Janeiro [Brasil] = Pontifical Catholic University of Rio de Janeiro [Brazil] = Université catholique pontificale de Rio de Janeiro [Brésil]

We review the proof of the hydrodynamic limit for the velocity-flip model which is given in [12]. We study the diffusive scaling limit for a chain of N coupled harmonic oscillators. In order to provide the system with good ergodic properties, we perturb the Hamiltonian dynamics with random flips of velocities, so that the energy is still conserved. We derive the hydrodynamic equations by estimating the relative entropy with respect to the local equilibrium state modified by a correction term.

Mots clés: Hydrodynamic limit; Hamiltonian system; Velocity-flip model

Domaines: Probabilités [math.PR]

Marielle Simon. Hydrodynamic limit for the velocity-flip model. Cédric Bernardin and Patricia Gonçalves. From Particle Systems to Partial Differential Equations I, France. 75, Springer Berlin Heidelberg, pp.269-284, 2013, From Particle Systems to Partial Differential Equations, 978-3-642-54270-1. ⟨10.1007/978-3-642-54271-8⟩. ⟨hal-01104050⟩