Speaker: Davide Augusto Bignamini (Università degli studi dell'Insubria.)

Titolo: Pathwise uniqueness for stochastic PDEs with singular locally Hölder-continuous drift 

Abstract: This talk is based on the paper [1]. The main focus is pathwise uniqueness for mild solutions to stochastic PDEs with a Hölder-continuous perturbation in the drift, given in differential form. The singularity of the drift perturbation allows to achieve novel pathwise uniqueness results for several classes of examples, ranging from fluid-dynamics to phase-separation models, previously studied only in the context of weak uniqueness, see [2,3]. 
References:
[1]D. Addona, D. A. Bignamini, C. Orrieri, L. Scarpa, Pathwise uniqueness by noise for singular stochastic PDEs, e-print arXiv:2512.17736, 2025.
[2] F. Bertacco, C. Orrieri, L. Scarpa, Weak uniqueness by noise for singular stochastic PDES, Transactions of the American Mathematical Society 378, 7977-8023 (2025).
[3]E. Priola, An optimal regularity result for Kolmogorov equations and weak uniqueness for some critical SPDEs, Annals of Probability 49, 1310–1346 (2021).