Spectral Closure and Non-Local Hydrodynamics for Kinetic Equations

The closure problem for kinetic equations constitutes one of the fundamental questions in thermodynamics. Based on the refined spectral theory of several kinetic models, involving a finite-dimensional Grad system, the Boltzmann-BGK equation and the Shakhov model, we give exact closure relations and transport operators for the hydrodynamic moments (density, velocity and pressure). This allows us to derive a new, non-local fluid model for gaseous fluid in the linear regime, which extends classical models such as the Navier―Stokes equation.