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arXiv · 2512.17736

Pathwise uniqueness by noise for singular stochastic PDEs

Davide Addona·Davide Bignamini·Carlo Orrieri·Luca Scarpa
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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.

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Davide Addona, Davide Bignamini, Carlo Orrieri, Luca Scarpa. 2025-12-19. Pathwise uniqueness by noise for singular stochastic PDEs. https://arxiv.org/abs/2512.17736

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