Dear Colleagues, We would like to invite you to the following SPASS seminars, *Some results on the Kraichnan model* by Umberto Pappalettera (Universität Basel) on Tuesday 20.1.2026 at 14:00 CET in Aula Magna, Dipartimento di Matematica, UNIPI. Online participants may join the seminar at https://meet.google.com/ajh-zrxc-wds Best, F. Butori on behalf of the organizers https://sites.google.com/unipi.it/spass ------------------- Abstract: We discuss a number of properties of ``turbulent'' solutions to the Kraichnan model constructed by Le Jan and Raimond in [Ann. Probab. 30(2): 826-873, 2002]. We cover the full range of compressibility ratios giving spontaneous stochasticity of particle trajectories. More specifically, we prove generic anomalous dissipation of the mean energy and fractional Sobolev regularity of solutions, for every square-integrable initial datum. The proof of the latter is obtained as a consequence of a new sharp regularity result for the degenerate parabolic PDE satisfied by the associated two-point self-correlation function, which is of independent interest.