The Vlasov Equation with Infinite Mass

We discuss about the initial value problem for the Vlasov equation in case of unbounded total mass. The problem strongly depends on the dimension d of the physical space and on the singularity of the interaction. In particular, for d = 3, the more singular the interaction, the faster must be the spatial decay at infinity of the initial distribution. We describe also an application which gives rise to a viscous friction model