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.
Conservative stochastic pde and fluctuations of the symmetric simple exclusion process
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Constructs weak solutions, proves anisotropic Besov regularity, and establishes uniqueness in the mass-preserving renormalized class for kinetic FP equations with nonlinear diffusion under mass-critical growth on Ψ.
Pathological trajectories appear with finite rate in the large deviations of the KMP process for d ≥ 2, with validation of a prior lower bound.
Reduced SPDE models for co-evolving opinion dynamics capture clustering behavior efficiently with lower cost than full-state models.
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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.
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Kinetic Fokker-Planck Equations with Nonlinear Diffusion
Constructs weak solutions, proves anisotropic Besov regularity, and establishes uniqueness in the mass-preserving renormalized class for kinetic FP equations with nonlinear diffusion under mass-critical growth on Ψ.
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Pathological Large Deviations of the KMP Process in Dimension $d\ge 2$
Pathological trajectories appear with finite rate in the large deviations of the KMP process for d ≥ 2, with validation of a prior lower bound.
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Clustering in co-evolving opinion dynamics: reduced SPDE models
Reduced SPDE models for co-evolving opinion dynamics capture clustering behavior efficiently with lower cost than full-state models.