  Vlasov equations can be formally derived from N-body dynamics in the
mean-field limit. In some suitable singular limits, they may themselves
converge to fluid dynamics equations. Motivated by this heuristic, we introduce
natural scalings under which the incompressible Euler equations can be
rigorously derived from N-body dynamics with repulsive Coulomb interaction. Our
analysis is based on the modulated energy methods of Brenier and Serfaty.
