Uniform in time lower bound for solutions to a quantum Boltzmann equation of bosons
Analysis of PDEs
2018-06-11 v3 Mathematical Physics
math.MP
Abstract
We consider the quantum Boltzmann equation, which describes the growth of the condensate, or in other words, models the interaction between excited atoms and a condensate. In this work, the full form of Bogoliubov dispersion law is considered, which leads to a detailed study of surface integrals inside the collision operator on energy manifolds. We prove that positive radial solutions of the quantum Boltzmann equation are bounded from below by a Gaussian, uniformly in time.
Keywords
Cite
@article{arxiv.1605.07890,
title = {Uniform in time lower bound for solutions to a quantum Boltzmann equation of bosons},
author = {Toan T. Nguyen and Minh-Binh Tran},
journal= {arXiv preprint arXiv:1605.07890},
year = {2018}
}