Well-posedness of the Dean–Kawasaki and the nonlinear Dawson–Watanabe equation with correlated noise
- Authors: Benjamin Fehrman, Benjamin Gess
- Preprint year: 2021
- First public date: 2021-08-19
- arXiv: 2108.08858
- Status: Published
- Publication type: Journal article
- Publication year: 2024
- Journal: Archive for rational mechanics and analysis, 248 (2024) 2, p. 20
- DOI: 10.1007/s00205-024-01963-3
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.