We would like to invite you to the following SPASS seminar, jointly organized by UniPi, SNS, UniFi (abstract below):

We discuss the behavior of the ordinary differential equations, flow maps, and continuity equations associated to autonomous random velocity fields that admit a natural multiscale finite range decomposition. The velocity fields we consider are only Hölder regular in space, and thus the associated ODE and continuity equation are not a priori well-posed. However, above the critical threshold of 1/2, due to multiscale stochastic cancellations, we show well-posedness is almost surely restored away from the zero level set of the velocity field. This threshold marks a genuine transition, as demonstrated by examples lying below the threshold that exhibit robust ill-posedness.

Best regards

Mario Maurelli