Global well-posedness of the quantum Boltzmann equation for bosons interacting via inverse power law potentials

TL;DR

This paper proves the global well-posedness of the quantum Boltzmann equation for bosons with singular collision kernels, modeling large systems of Bose-Einstein particles interacting via inverse power law potentials, near equilibrium in a periodic domain.

Contribution

It establishes the first global well-posedness result for the quantum Boltzmann equation with inverse power law interactions near equilibrium.

Findings

Global well-posedness in a periodic box

Results valid near high-temperature equilibrium

Handles singular collision kernels

Abstract

We consider the spatially inhomogeneous quantum Boltzmann equation for bosons with a singular collision kernel, the weak-coupling limit of a large system of Bose-Einstein particles interacting through inverse power law. Global well-posedness of the corresponding Cauchy problem is proved in a periodic box near equilibrium for initial data satisfying high temperature condition.