  In this work we prove the nonlinear instability of inhomogeneous steady
states solutions to the Hamiltonian Mean Field (HMF) model. We first study the
linear instability of this model under a simple criterion by adapting the
techniques developed in [19]. In a second part, we extend to the inhomogeneous
case some techniques developed in [14, 17, 18] and prove a nonlinear
instability result under the same criterion.
