On the Cauchy problem with large data for a space-dependent Boltzmann-Nordheim boson equation

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. The solutions either explode in the $L^{\infty }$-norm in finite time, or exist globally in time. They are obtained as limits of solutions to corresponding anyon equations.

19 pages. arXiv admin note: text overlap with arXiv:1406.0265