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math.PR2026

Dean-Kawasaki Equation with Biot-Savart and Keller-Segel Interactions: Existence and Large Deviations

Xiaohao Ji, Yue Sun, Zhengyan Wu

We establish the existence of probabilistically weak, renormalized kinetic solutions to the Dean--Kawasaki equation with singular interaction kernels, including those of Biot--Sava…