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

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  • Popat, Shyam

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.

Suggested Citation

  • Popat, Shyam, 2025. "Well-Posedness of the generalised Dean–Kawasaki Equation with correlated noise on bounded domains," Stochastic Processes and their Applications, Elsevier, vol. 179(C).
  • Handle: RePEc:eee:spapps:v:179:y:2025:i:c:s0304414924002114
    DOI: 10.1016/j.spa.2024.104503
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