The hydrodynamic limit for local mean-field dynamics with unbounded spins

We consider the dynamics of a class of spin systems with unbounded spins interacting with local mean field interactions. We proof convergence of the empirical measure to the solution of a McKean-Vlasov equation in the hydrodynamic limit and propagation of chaos. This extends earlier results of G"artner, Comets and others for bounded spins or strict mean field interactions.