English

Pathwise uniqueness by noise for singular stochastic PDEs

Probability 2025-12-22 v1 Analysis of PDEs

Abstract

Pathwise uniqueness for stochastic PDEs with drift in differential form is a main open problem in the recent literature on regularisation by noise. This paper establishes a self-contained theory in the framework of stochastic evolution equations on separable Hilbert spaces and provides a first result to address such an issue. The singularity of the drift allows to achieve novel uniqueness results for several classes of examples, ranging from fluid-dynamics to phase-separation models.

Keywords

Cite

@article{arxiv.2512.17736,
  title  = {Pathwise uniqueness by noise for singular stochastic PDEs},
  author = {Davide Addona and Davide Bignamini and Carlo Orrieri and Luca Scarpa},
  journal= {arXiv preprint arXiv:2512.17736},
  year   = {2025}
}

Comments

47 pages

R2 v1 2026-07-01T08:33:45.957Z