We derive the hydrodynamic limit of a kinetic equation where the interactions in
velocity are modeled by a linear operator (Fokker–Planck or linear Boltzmann) and
the force in the Vlasov term is a stochastic process with high amplitude and
short-range correlation. In the scales and the regime we consider, the hydrodynamic
equation is a scalar second-order stochastic partial differential equation.
Compared to the deterministic case, we also observe a phenomenon of enhanced
diffusion.
