Bose condensate inb interaction with excitations - a two-component space-dependent model close to equilibrium

TL;DR

This paper develops a two-component model describing the interaction between Bose-Einstein condensates and excitations near the critical temperature, analyzing well-posedness and long-term behavior.

Contribution

It introduces a coupled kinetic-Gross-Pitaevskii model for Bose gases near the condensation temperature, with new results on well-posedness and stability.

Findings

Proved well-posedness of the model near equilibrium

Analyzed long-time behavior of the system

Established stability results in an H1-setting

Abstract

The paper considers a model for Bose gases in the so-called 'high-temperature range' below the temperature Tc, where Bose-Einstein condensation sets in.The model is of non-linear two-component type, consisting of a kinetic equation with periodic boundary conditions for the distribution function of a gas of excitations interacting with a Bose condensate, which is described by a Gross-Pitaevskii equation. Results on well-posedness and long time behaviour are proved in a H1-setting close to equilibrium.