On the linearized system of equations for the condensate-normal fluid interaction near the critical temperature

TL;DR

This paper analyzes the linearized equations governing condensate-normal fluid interactions near the critical temperature, proving global solutions, conservation laws, and describing long-term behavior in a kinetic theory context.

Contribution

It provides the first rigorous analysis of the linearized system near the critical temperature, establishing existence, regularity, and asymptotic properties of solutions.

Findings

Global classical solutions exist for radially symmetric initial data.

Solutions satisfy natural conservation laws.

Long-time asymptotic behavior is characterized.

Abstract

The Cauchy problem for the linearization of a system of equations arising in the kinetic theory of a condensed gas of bosons near the critical temperature around one of its equilibria is solved for radially symmetric initial data. It is proved that the linearized system has global classical solutions that satisfy the natural conservation laws for a large set of initial data. Some regularity properties of the solutions and their long time asymptotic behavior are described.