Pith. sign in

REVIEW 3 cited by

Well-posedness of Dean-Kawasaki Equation with Singular Interactions

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2207.12774 v4 pith:FOCNX4AJ submitted 2022-07-26 math.PR

Likun Wang , Zhengyan Wu , Rangrang Zhang This is my paper · ORCID
classification math.PR
keywords equationwell-posednessdean-kawasakifehrmanfluctuatinggessinteractioninteractions
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

Inspired by [Fehrman, Gess; Invent. Math., 2023] and [Fehrman, Gess; Arch. Ration. Mech. Anal., 2024], we consider the Dean-Kawasaki equation with singular interactions and correlated noise which can be viewed as fluctuating mean-field limits. By imposing the Ladyzhenskaya-Prodi-Serrin condition on the interaction kernel, the existence of probabilistic weak renormalized kinetic solutions is established. Further, under an additional integrability assumption on the divergence of the interaction kernel, a kinetic formulation approach is applied to derive pathwise uniqueness, leading to the strong well-posedness of the equation. As an application, we obtain the well-posedness of a conservative stochastic partial differential equation known as the fluctuating Ising-Kac-Kawasaki dynamics.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Kinetic Theory with Fluctuations: Strong Well-Posedness of the Vlasov-Fokker-Planck-Dean-Kawasaki System

    math.PR 2025-11 unverdicted novelty 7.0 of 10

    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.

  2. Kinetic Fokker-Planck Equations with Nonlinear Diffusion

    math.AP 2026-07 unverdicted novelty 6.0 of 10

    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.

  3. The Dean-Kawasaki equation and stochastic density functional theory

    cond-mat.soft 2024-11 accept novelty 2.0 of 10

    A review of the Dean-Kawasaki equation and stochastic density functional theory, covering derivation, mathematical issues, extensions, solution methods, and applications.

Pith tools