2006/05/11 by S. Mischler, Stéphane Mischler, Clément Mouhot +2 · 3 citations
Engineering · Mathematics · Physics and Astronomy · #Boltzmann equation #Cauchy distribution #Cauchy problem #Classical mechanics #Collision #Gas Dynamics and Kinetic Theory #Hard spheres #Inelastic collision #Initial value problem #Mathematical analysis #Mathematics #Navier-Stokes equation solutions #Particle Dynamics in Fluid Flows #Physics #Quantum mechanics #SPHERES #Smoothness #Thermodynamics #Uniqueness #math-ph #math.AP #math.MP #msc:76P05 #msc:82B40 #msc:82C40
paper · pdf · doi:10.1007/s10955-006-9096-9
published as Journal of Statistical Physics 124 (2006) 655-702 · 45 pages
openalex publication_date 2006/05/11 · arxiv created 2006/07/21 · arxiv updated 2016/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitution coefficients depending on the kinetic energy and the relative velocity as well as the sticky particles model. We prove (local in time) non-concentration estimates in Orlicz spaces, from which we deduce weak stability and existence theorem. Strong stability together with uniqueness and instantaneous appearance of exponential moments are proved under additional smoothness assumption on the initial datum, for a restricted class of collision rates. Concerning the long-time behaviour, we give conditions for the cooling process to occur or not in finite time.