Weak solutions to granular medium equations via stochastic particle approximations

We establish weak existence for McKean–Vlasov stochastic differential equations associated with granular medium equations with porous medium diffusion, for m>1 in arbitrary dimension. The result covers a class of nonconvex potentials with locally Lipschitz gradients of polynomial growth. Our particle approximation generates nonlinear diffusion through density-dependent noise and allows initial densities with finite Boltzmann entropy but infinite internal energy.