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Dean-Kawasaki dynamics: ill-posedness vs. triviality. (English) Zbl 1406.60095
Summary: 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.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60G57 Random measures
43A35 Positive definite functions on groups, semigroups, etc.
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
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