Year: 2026
Type: article
Abstract: . Inspired by [Fehrman and Gess, Invent. Math., 234 (2023), pp. 573–636] and [Fehrman and Gess, Arch. Ration. Mech. Anal., 248 (2024), 20], 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.
DOI: 10.1137/25m1743818
Authors: Likun Wang, Zhengyan Wu, Rangrang Zhang
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: Deutsche Forschungsgemeinschaft, National Natural Science Foundation of China, Chinese Academy of Sciences, Beijing Institute of Technology, Ministry of Industry and Information Technology of the People's Republic of China, Beijing Institute of Technology Research Fund Program for Young Scholars, Division of Mathematical Sciences
OpenAlex ID: W4288727212