Well-Posedness of the Dean–Kawasaki and the Nonlinear Dawson–Watanabe Equation with Correlated Noise

Document Type

Article

Publication Date

4-1-2024

Abstract

In this paper we prove the well-posedness of the generalized Dean–Kawasaki equation driven by noise that is white in time and colored in space. The results treat diffusion coefficients that are only locally 1/2-Hölder continuous, including the square root. This solves several open problems, including the well-posedness of the Dean–Kawasaki equation and the nonlinear Dawson–Watanabe equation with correlated noise.

Publication Source (Journal or Book title)

Archive for Rational Mechanics and Analysis

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