Regularization by Noise for the Stochastic Transport Equation

Explore a 57-minute lecture on regularization by noise for the stochastic transport equation, presented by Lisa Beck at the Hausdorff Center for Mathematics. Delve into the intricacies of weak (L∞-) solutions for both deterministic and stochastic transport equations, examining the interplay between drift, unknown variables, and Brownian motion. Discover how the introduction of stochastic elements can prevent non-uniqueness and singularities, even with less regular drift conditions. Compare techniques used for deterministic equations with PDE approaches for stochastic cases. Gain insights into the conservation of Sobolev regularity and the restoration of uniqueness in stochastic transport equations. Learn about the Ladyzhenskaya–Prodi–Serrin condition and its significance in fluid dynamics and equation solvability. Understand the collaborative research efforts behind these findings, involving F. Flandoli, M. Gubinelli, and M. Maurelli.