Title: Quantum hydrodynamic approximations to the finite temperature trapped Bose gases,
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.