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

TL;DR

This paper establishes existence, uniqueness, and stability of solutions to a space-dependent Boltzmann-Nordheim boson equation with large initial data, highlighting conditions for finite-time blow-up or global existence.

Contribution

It provides the first rigorous analysis of large data solutions for the Boltzmann-Nordheim boson equation in a space-dependent setting, including solution behavior and limits from anyon equations.

Findings

Solutions conserve mass, momentum, and energy.

Solutions may blow up in finite time or exist globally.

Solutions are limits of corresponding anyon equations.

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.