  A wide range of phenomena in the natural and social sciences involve large
systems of interacting particles, including plasmas, collections of galaxies,
coupled oscillators, cell aggregations, and economic ``agents'. Kinetic methods
for reducing the complexity of such systems typically involve the derivation of
nonlinear partial differential equations for the corresponding global
densities. In recent years there has been considerable interest in the mean
field limit of interacting particle systems with long range interactions. Two
major examples are interacting Brownian particles in the overdamped regime and
the Kuramoto model of coupled phase oscillators. In this paper we analyze these
systems in the presence of local or global stochastic resetting, where the
position or phase of each particle independently or simultaneously resets to
its original value at a random sequence of times generated by a Poisson
process. In each case we derive the Dean-Kawasaki (DK) equation describing
hydrodynamic fluctuations of the global density, and then use a mean field
ansatz to obtain the corresponding nonlinear McKean-Vlasov (MV) equation in the
thermodynamic limit. In particular, we show how the MV equation for global
resetting is driven by a Poisson shot noise process, reflecting the fact that
resetting is common to all of the particles and thus induces correlations that
cannot be eliminated by taking a mean field limit. We then investigate the
effects of local and global resetting on nonequilibrium stationary solutions of
the macroscopic dynamics and, in the case of the Kuramoto model, the reduced
dynamics on the Ott-Antonsen manifold.
