  In the Vlasov-Poisson equation, every configuration which is homogeneous in
space provides a stationary solution. Penrose gave in 1960 a criterion for such
a configuration to be linearly unstable. While this criterion makes sense in a
measure-valued setting, the existing results concerning nonlinear instability
always suppose some regularity with respect to the velocity variable. Here,
thanks to a multiphasic reformulation of the problem, we can prove an "almost
Lyapounov instability" result for the Vlasov-Poisson equation, and an
ill-posedness result for the kinetic Euler equation and the Vlasov-Benney
equation (two quasineutral limits of the Vlasov-Poisson equation), both around
any unstable measure.
