Hydrodynamic Limit for a Hamiltonian System with Boundary Conditions and Conservative Noise

Olla, Stefano; Even, Nadine

Olla, Stefano; Even, Nadine (2014), Hydrodynamic Limit for a Hamiltonian System with Boundary Conditions and Conservative Noise, Archive for Rational Mechanics and Analysis, 213, 2, p. 561-585. http://dx.doi.org/10.1007/s00205-014-0741-1

Type

Article accepté pour publication ou publié

External document link

http://fr.arXiv.org/abs/1009.2175

Date

2014

Journal name

Archive for Rational Mechanics and Analysis

Volume

213

Number

Publisher

Springer

Pages

561-585

Abstract (EN)

We study the hyperbolic scaling limit for a chain of N coupled anharmonic oscillators. The chain is open and with the following adiabatic boundary conditions: it is attached to a wall on the left and there is a force (tension) $\tau$ acting on the right.In order to provide the system of the good ergodic properties, we perturb the Hamiltonian dynamics with random local exchanges of velocities between the particles, so that momentum and energy are locally conserved. We prove that in the macroscopic limit the distribution of the density of particles, momentum and energy converge to the solution of the Euler equations, in the smooth regime of them.

Subjects / Keywords

adiabatic boundary conditions; entropy production; relative entropy; Euler equation; hydrodynamic limit