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.
From: Zhengyan Wu [view email]
[v1]
Tue, 26 Jul 2022 09:46:10 UTC (73 KB)
[v2]
Wed, 27 Jul 2022 03:56:56 UTC (72 KB)
[v3]
Sun, 21 Apr 2024 05:57:34 UTC (97 KB)
[v4]
Tue, 30 Jun 2026 14:41:22 UTC (102 KB)
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