2007/03/02 by Jean Bricmont, Antti Kupiainen, A. Kupiainen
Materials Science · Mathematics · Physics and Astronomy · #Gas Dynamics and Kinetic Theory #Numerical methods in inverse problems #Thermal properties of materials #math-ph #math.MP #msc:82C70
paper · pdf · doi:10.1007/s00220-008-0480-y
23 pages
arxiv created 2007/03/02 · openalex publication_date 2008/04/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We study the asymptotics of solutions of the Boltzmann equation describing the kinetic limit of a lattice of classical interacting anharmonic oscillators. We prove that, if the initial condition is a small perturbation of an equilibrium state, and vanishes at infinity, the dynamics tends diffusively to equilibrium. The solution is the sum of a local equilibrium state, associated to conserved quantities that diffuse to zero, and fast variables that are slaved to the slow ones. This slaving implies the Fourier law, which relates the induced currents to the gradients of the conserved quantities.