# Quantum hydrodynamic approximations to the finite temperature trapped Bose gases

## TL;DR

This paper derives hydrodynamic models, including Euler and Navier-Stokes equations, for finite temperature trapped Bose gases using quantum kinetic theory and Chapman-Enskog expansion, aligning with Landau's two fluid theory.

## Contribution

It introduces a systematic derivation of hydrodynamic equations for Bose-Einstein condensates at finite temperature, capturing condensate and non-condensate interactions.

## Key findings

- Hydrodynamic models agree with Landau's two fluid theory.
- Derivation includes both Euler and Navier-Stokes approximations.
- Models describe macroscopic behavior and condensate-non-condensate coupling.

## Abstract

For the quantum kinetic system modelling the Bose-Einstein Condensate that accounts for interactions between condensate and excited atoms, we use the Chapman-Enskog expansion to derive its hydrodynamic approximations, include both Euler and Navier-Stokes approximations. The hydrodynamic approximations describe not only the macroscopic behavior of the BEC but also its coupling with the non-condensates, which agrees with Landau's two fluid theory.