An explicit coercivity estimate of the linearized quantum Boltzmann operator without angular cutoff
Abstract
The quantum Boltzmann-Bose equation describes a large system of Bose-Einstein particles in the weak-coupling regime. If the particle interaction is governed by the inverse power law, the corresponding collision kernel has angular singularity. In this paper, we give a constructive proof of the coercivity estimate for the linearized quantum Boltzmann-Bose operator to capture the effects of the singularity and the fugacity. Precisely, the estimate explicitly reveals the dependence on the fugacity parameter before the Bose-Einstein condensation. With the coercivity estimate, the global in time well-posedness of the inhomogeneous quantum Boltzmann-Bose equation in the perturbative framework and stability of the Bose-Einstein equilibrium can be established.
Keywords
Cite
@article{arxiv.2212.03531,
title = {An explicit coercivity estimate of the linearized quantum Boltzmann operator without angular cutoff},
author = {Tong Yang and Yu-Long Zhou},
journal= {arXiv preprint arXiv:2212.03531},
year = {2022}
}