2006/05/11 by S. Mischler, Stéphane Mischler, Clément Mouhot · 76 citations
Engineering · Mathematics · Physics and Astronomy · #Algebraic number #Boltzmann constant #Boltzmann equation #Classical mechanics #Context (archaeology) #Gas Dynamics and Kinetic Theory #Gravitational singularity #Hard spheres #Isotropy #Mathematical analysis #Mathematics #Navier-Stokes equation solutions #Particle Dynamics in Fluid Flows #Physics #Pointwise #Quantum mechanics #SPHERES #Statistical physics #Thermodynamics #math-ph #math.AP #math.MP #msc:76P05 #msc:82B40 #msc:82C40
paper · pdf · doi:10.1007/s10955-006-9097-8
published in Journal of Statistical Physics 124(2-4), 703-746 (Springer Science+Business Media) · 41 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 consider the spatially homogeneous Boltzmann equation for inelastic hard spheres, in the framework of so-called constant normal restitution coefficients. We prove the existence of self-similar solutions, and we give pointwise estimates on their tail. We also give general estimates on the tail and the regularity of generic solutions. In particular we prove Haff 's law on the rate of decay of temperature, as well as the algebraic decay of singularities. The proofs are based on the regularity study of a rescaled problem, with the help of the regularity properties of the gain part of the Boltzmann collision integral, well-known in the elastic case, and which are extended here in the context of granular gases.