Dean-Kawasaki dynamics: ill-posedness vs. triviality

Konarovskyi V, Lehmann T, von Renesse M-K. Dean-Kawasaki dynamics: ill-posedness vs. triviality. Electronic Communications in Probability. 2019;24: 8.We prove that the Dean-Kawasaki SPDE admits a solution only in integer parameter regimes, in which case the solution is given in terms of a system of non-interacting particles