This is the second part of the talk from last Monday:
The α-Riccati equation is a differential equation that features a non-local quadratic nonlinearity coupled with a dissipative linear term and can be viewed as a toy problem for Navier-Stokes-like systems. In this series of talks I will discuss how stochastic cascade approach pioneered by Le Jan and Sznitmann (1997) can be used to establish both lack of uniqueness and finite-time blow up for large initial data in the case α>1. In particular we will discover how explosion of the associated stochastic cascade leads to the lack of uniqueness of global solutions for any choice of initial data.
Based on joint work with E. Thomann and E. Waymire.