Contents Online
Communications in Mathematical Sciences
Volume 19 (2021)
Number 2
Asymptotic analysis of the Boltzmann equation with very soft potentials from angular cutoff to non-cutoff
Pages: 287 – 324
DOI: https://dx.doi.org/10.4310/CMS.2021.v19.n2.a1
Authors
Abstract
Our focus is the Boltzmann equation in a torus under very soft potentials around equilibrium. We analyze the asymptotics of the equation from angular cutoff to non-cutoff. We first prove a refined decay result of the semi-group stemming from the linearized Boltzmann operator. Then we prove the global well-posedness of the equations near equilibrium, refined decay patterns of the solutions. Finally, we rigorously give the asymptotic formula between the solutions to cutoff and noncutoff equations with an explicit convergence rate.
Keywords
Boltzmann equation, very soft potential, asymptotic analysis, angular cutoff, angular non-cutoff, short-range interaction, long-range interaction
2010 Mathematics Subject Classification
35B40, 35Q20, 82C40
Received 8 June 2020
Accepted 25 August 2020
Published 12 April 2021