Well-Posedness of Dean–Kawasaki Equation with Singular Interactions
Abstract
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.
Fields of Study & Subjects
Advanced Mathematical Physics Problems
Stochastic processes and statistical mechanics
Fractional Differential Equations Solutions
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Volume
- 58
- Issue
- 3
- Pages
- 2738–2785
- Publication date
- 28 May 2026
- Language
- EN