Well-Posedness of the generalised Dean–Kawasaki Equation with correlated noise on bounded domains

Shyam Popat

Stochastic Processes and their Applications, 2025, vol. 179, issue C

Abstract: In this paper, we extend the notion of stochastic kinetic solutions introduced in Fehrman and Gess (2024) to establish the well-posedness of stochastic kinetic solutions of generalised Dean–Kawasaki equations with correlated noise on bounded, C2-domains with Dirichlet boundary conditions. The results apply to a wide class of non-negative boundary data, which is based on certain a priori estimates for the solutions, that encompasses all non-negative constant functions including zero and all smooth functions bounded away from zero.

Keywords: Stochastic partial differential equation; Dean–Kawasaki equation; Dirichlet boundary conditions (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2024.104503

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