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arXiv · 2108.08858

Well-posedness of the Dean--Kawasaki and the nonlinear Dawson--Watanabe equation with correlated noise

Benjamin Fehrman·Benjamin Gess
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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-H\"older 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.

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Benjamin Fehrman, Benjamin Gess. 2021-08-19. Well-posedness of the Dean--Kawasaki and the nonlinear Dawson--Watanabe equation with correlated noise. https://arxiv.org/abs/2108.08858

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