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Conservative stochastic PDEs on the whole space

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arxiv 2410.00254 v1 pith:JAPFI6CL submitted 2024-09-30 math.PR math.AP

Benjamin Fehrman , Benjamin Gess This is my paper · ORCID
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keywords stochasticconservativefluctuatinghydrodynamicspdesspacetheorywhole
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The purpose of this paper is to establish a well-posedness theory for conservative stochastic partial differential equations on the whole space. This class of stochastic PDEs arises in fluctuating hydrodynamics, and includes the Dean--Kawasaki equation with correlated noise. In combination with the analysis of the authors and Heydecker [35], the connection between fluctuating hydrodynamics and macroscopic fluctuation theory in the context of the zero range particle process is made rigorous.

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  1. Ill-posedness of the pure-noise Dean-Kawasaki equation

    math.PR 2025-01 conditional novelty 7.0 of 10

    The pure-noise Dean-Kawasaki equation with any bounded drift has no measure-valued martingale solutions.

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