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Hydrodynamic limit for a chain with thermal and mechanical boundary forces

Komorowski, Tomasz; Olla, Stefano; Simon, Marielle (2021), Hydrodynamic limit for a chain with thermal and mechanical boundary forces, Electronic Journal of Probability, 26, p. 1-49. 10.1214/21-EJP581

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Type
Article accepté pour publication ou publié
Date
2021
Nom de la revue
Electronic Journal of Probability
Volume
26
Éditeur
Institute of Mathematical Statistics
Pages
1-49
Identifiant publication
Métadonnées
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Auteur(s)
Komorowski, Tomasz
Institut of Mathematics - Polish Academy of Sciences [PAN]
Olla, Stefano cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Simon, Marielle
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Résumé (EN)
We prove the hydrodynamic limit for a one dimensional harmonic chain with a random flip of the momentum sign. The system is open and subject to two thermostats at the boundaries and to an external tension at one of the endpoints. Under a diffusive scaling of space-time, we prove that the empirical profiles of the two locally conserved quantities, the volume stretch and the energy, converge to the solution of a non-linear diffusive system of conservative partial differential equations.
Mots-clés
Boundary conditions; Fourier-Wigner functions; Harmonic chain; Hydrodynamic limit