Conservative stochastic PDEs on the whole space

• Authors: Benjamin Fehrman, Benjamin Gess
• First public date: 2024-09-30
• arXiv: 2410.00254
• Preprint year: 2024
• Status: Published
• Publication type: Journal article
• Publication year: 2026
• Journal: Stochastics and partial differential equations : analysis and computations, 14 (2026) 1, pp. 350-388
• DOI: 10.1007/s40072-025-00369-w

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.

Associated SAiS members

• Benjamin Gess

Associated projects

• FluCo

Research areas

• SPDEs
• Non-equilibrium Statistical Mechanics, Interacting Particle Systems and Fluctuating Hydrodynamics

BibTeX

@article{arxiv241000254,
  title = {Conservative stochastic PDEs on the whole space},
  author = {Benjamin Fehrman and Benjamin Gess},
  year = {2026},
  journal = {Stochastics and partial differential equations : analysis and computations, 14 (2026) 1, pp. 350-388},
  doi = {10.1007/s40072-025-00369-w},
  eprint = {2410.00254},
  archivePrefix = {arXiv},
  primaryClass = {math.PR}
}