  We give an explicit description of the spectral closure for the
three-dimensional linear Boltzmann-BGK equation in terms of the macroscopic
fields, density, flow velocity and temperature. This results in a new linear
fluid dynamics model which is valid for any relaxation time. The non-local
exact fluid dynamics equations are compared to the Euler, Navier--Stokes and
Burnett equations. Our results are based on a detailed spectral analysis of the
linearized Boltzmann-BGK operator together with a suitable choice of spectral
projection.
