The Vlasov–Fokker–Planck–Dean–Kawasaki equation with correlated noise and bounded nonlocal interactions has a unique probabilistically strong renormalized kinetic solution for finite-mass, finite-entropy initial data.
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Kinetic Theory with Fluctuations: Strong Well-Posedness of the Vlasov-Fokker-Planck-Dean-Kawasaki System
The Vlasov–Fokker–Planck–Dean–Kawasaki equation with correlated noise and bounded nonlocal interactions has a unique probabilistically strong renormalized kinetic solution for finite-mass, finite-entropy initial data.