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arXiv · 2403.19466

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

Shyam Popat
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Abstract

In this paper, we extend the notion of stochastic kinetic solutions introduced in arXiv:2108.08858 to establish the well-posedness of stochastic kinetic solutions of generalized Dean-Kawasaki equations with correlated noise on bounded, $C^2$-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.

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Shyam Popat. 2024-03-28. Well-Posedness of the generalised Dean-Kawasaki Equation with correlated noise on bounded domains. https://doi.org/10.1016/j.spa.2024.104503

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