Résumé : In this talk I will present a couple of results for the existence of solutions to the one-dimensional Euler, Navier-Stokes and multi-dimensional Navier-Stokes systems. The purpose of the talk is to focus on the role of the pressure in the compressible fluid equations, and to understand whether or not it can be replaced by the nonlocal attraction-repulsion terms arising in the models of collective behaviour.

Keywords : Navier-Stokes equations; singular limits; non-local forces