Hydrodynamic Limit for a Hamiltonian System with Boundary Conditions and Conservative Noise
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
TypeArticle accepté pour publication ou publié
External document linkhttp://fr.arXiv.org/abs/1009.2175
Journal nameArchive for Rational Mechanics and Analysis
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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 / Keywordsadiabatic boundary conditions; entropy production; relative entropy; Euler equation; hydrodynamic limit
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