Contents Online
Communications in Mathematical Sciences
Volume 15 (2017)
Number 5
On the Cauchy problem with large data for a space-dependent Boltzmann–Nordheim boson equation
Pages: 1247 – 1264
DOI: https://dx.doi.org/10.4310/CMS.2017.v15.n5.a4
Authors
Abstract
This paper studies a Boltzmann–Nordheim equation in a slab with two-dimensional velocity space and pseudo-Maxwellian forces. Strong solutions are obtained for the Cauchy problem with large initial data in an $L^1 \cap L^{\infty}$ setting. The main results are existence, uniqueness and stability of solutions conserving mass, momentum and energy that explode in $L^{\infty}$ if they are only local in time. The solutions are obtained as limits of solutions to corresponding anyon equations.
Keywords
bosonic Boltzmann-Nordheim equation, low temperature kinetic theory, quantum Boltzmann equation
2010 Mathematics Subject Classification
82C10, 82C22, 82C40
Received 26 January 2016
Published 26 June 2017