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<p>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 [<CitationRef CitationID="CR1">1</CitationRef>], the connection between fluctuating hydrodynamics and macroscopic fluctuation theory in the context of the zero range particle process is made rigorous.</p>

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Conservative stochastic PDEs on the whole space

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月4日

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  • Benjamin Fehrman,
  • Benjamin Gess

摘要

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 [1], the connection between fluctuating hydrodynamics and macroscopic fluctuation theory in the context of the zero range particle process is made rigorous.