Abstract I will review the state of the art in Grad’s validity problem for a mathematical justification of fluid equations based on fundamental laws of classical mechanics. With the techniques currently available, such a problem can be faced in some simple case for perfect gases, using the kinetic theory of Boltzmann as an intermediate step. In particular I will discuss a recent result establishing the connection between microscopic and hydrodynamic scales, for perturbations of a global equilibrium.Funded by the European Union. Organizzatrice: Prof. Maria Groppi Locandina PDF Locandina Colloquium Simonella 2024