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# 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: http://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