Conservative stochastic PDEs on the whole space

Benjamin Fehrman; Benjamin Gess

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arXiv · 2410.00254

Conservative stochastic PDEs on the whole space

Benjamin Fehrman·Benjamin Gess

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Abstract

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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Benjamin Fehrman, Benjamin Gess. 2024-09-30. Conservative stochastic PDEs on the whole space. https://arxiv.org/abs/2410.00254

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