Mathematical tools for the derivation of hydrodynamic limits

Abstract

In all existing works on the subject, the general strategy to derive hydrodynamic limits is to proceed by analogy, that is to recognize the structure of the expected limiting hydrodynamic model in the corresponding scaled Boltzmann equation. This explains for instance why all hydrodynamic limits are not equally understood. The aim of this chapter is therefore to detail these analogies, focusing our attention on the point of view of functional analysis.