This seminar will be presented in hybrid mode. The speaker will deliver his talk in person.
Title: Finite-time explosion of the stochastic Katz-Pavlović model
Abstract: Abstract: In this talk, I will discuss a recent result on a dyadic model that was introduced by Katz and Pavlović. This model is a simplified version of the 3D Navier-Stokes system but shares with the latter some key properties such as the energy identity and scaling properties. It was shown by the seminal work of Katz and Pavlović that, for dissipation below some order, the model admits solutions that explode in finite-time. In a recent work in collaboration with Martin Hairer, we show that such explosion persists even when the equation is subject to an additive random noise. I will discuss the basic properties of the model, then go over the general explosion mechanism as well as the key arguments of our proof.