On the hydrodynamic closure of a transport-diffusion equation,

In this paper we discuss the passage to hydrodynamics for a transport diffusion equation. It is shown that the self-similar solution of the diffusion equation can be fruitfully used to construct the Euler equations for the model, provided the initial density possesses sufficiently many moments. The results of the paper can be of interest in dissipative kinetic theory, where the role of the homogeneous cooling state in the passage to hydrodynamics has been shown only from a formal point of view.