I will explain how a multiphase fluid formulation of Vlasov-type equations can be used to deal with (in)stability problems around stationary solutions that are only measures in velocity. It can be applied to the study of the instability of Vlasov-Poisson equations around rough profiles in velocity, or to the stability of Vlasov-Navier-Stokes equations around monokinetic profiles. This is a joint work with Aymeric Baradat (CNRS and Lyon 1) and Daniel Han-Kwan (CNRS and Nantes Université).