Seminario Ph.D. student Francesco Triggiano

Dissipative solutions to randomly forced 3D Euler equations

Ph.D. student Francesco Triggiano, Scuola Normale di Pisa.

Abstract: The purpose of this talk is twofold. First, we construct probabilistically strong solutions to the three-dimensional Euler equations perturbed by additive noise that are ℙ-almost surely continuous in time, Hölder in space, and satisfy the local energy inequality up to an arbitrarily large stopping time. Second, we prove several non-unique ergodicity results for the forced Euler equations with continuous-in-time external forcing. The solutions we construct are genuinely random and, almost surely, strictly dissipative and not steady states. This talk is based on joint work with Umberto Pappalettera.

Francesco Triggiano obtained his Bachelor’s degree in Mathematics from the University of Bari Aldo Moro in 2020, followed by a Master’s degree in Mathematics from the University of Pisa in 2022. He is currently a PhD student at Scuola Normale Superiore, in the program “Computational Methods and Mathematical Models for Sciences and Finance”, under the supervision of Prof. Marco Romito and Prof. Franco Flandoli. Starting in October 2026, he will join the Stochastic Analysis group at EPFL as a postdoctoral researcher. His research interests lie at the intersection of evolution equations and probability; in particular, he works on deterministic and stochastic differential equations, both PDEs and ODEs, arising in fluid dynamics and in the analysis of optimization algorithms widely used in machine learning.