Buongiorno a tutti, Vorremmo segnalarvi che venerdì prossimo (28 Novembre) alle 14:30 in aula 2BC30 (Torre Archimede, Università di Padova) ci sarà un seminario per il ciclo di seminari in Probabilità e Finanza di: Lucio Galeati (Università dell'Aquila) <https://sites.google.com/view/lucio-galeati-math/home> https://sites.google.com/view/lucio-galeati-math/home Title: Anomalous dissipation and anomalous regularization in the Kraichnan model of turbulence Date: November 28, 2025, at 14:30, 2BC30 Abstract: In the 60s Kraichnan proposed a synthetic model for passive scalar turbulence, consisting of a scalar advected by a random Gaussian velocity field, white in time and -Holder continuous in space. Despite its simplicity, this SPDE displays anomalous dissipation of energy, spontaneous stochasticity and intermittency, which are also expected for more realistic turbulent fluids. At the same time, solutions to the inviscid SPDE are unique and can be recovered by vanishing viscosity and mollification schemes. In this talk I will present some recent further understandings on this model: i) solutions to the transport equation with initial data display anomalous regularisation and almost gain Sobolev regularity , but not better; ii) solutions to the continuity equation starting from Dirac deltas instantaneously gain Lebesgue integrability, due to the diffusive behaviour of Lagrangian particle splitting, and their variance at small times grows like . Based on joint works with M. Maurelli, F. Grotto, U. Pappalettera and T. Drivas. Vi aspettiamo numerosi! Alberto Chiarini e Alekos Cecchin Sito web del seminario: https://www.math.unipd.it/~chiarini/seminars/
