On the linearized system of equations for the condensate-normal fluid interaction at very low temperature

TL;DR

This paper analyzes the linearized equations governing superfluid-normal fluid interactions in a Bose gas at very low temperatures, establishing conditions for global solutions and their convergence to equilibrium.

Contribution

It provides a new simple criterion for the existence of global solutions and demonstrates their convergence rates to stationary states in the low-temperature regime.

Findings

Necessary and sufficient condition for global solutions

Proof of convergence to stationary states

Quantitative rates of convergence for fluid components

Abstract

The linearization around one of its equilibrium of a system that describes the correlations between the superfluid component and the normal fluid part of a condensed Bose gas in the approximation of very low temperature and small condensate density, is studied. A simple and transparent argument gives a necessary and sufficient condition on the initial data for the existence of global solutions satisfying the conservation of the total number of particles and energy. Their convergence to a suitable stationary state is also shown and rates of convergence for the normal fluid and superfluid components are obtained.