Blow up in a 3-D "toy" model for the Euler equations

Topic:Blow up in a 3-D "toy" model for the Euler equations
Speaker:Susan Friedlander
Date:Monday, February 14
Time/Room:4:00pm - 5:00pm/S-101

We present a 3-D vector dyadic model given in terms of an infinite system of nonlinearly coupled ODE. This toy model is inspired by approximations to the fluid equations studied by Dinaburg and Sinai. The model has structural similarities with the Euler equations and it mimics certain important properties of the fluid equations, namely conservation of energy and divergence free velocity. We prove that for certain families of initial data blow-up occurs in the model system in the sense that the H^s, s > 3/2 , norm becomes unbounded in finite time. This is joint work with Natasa Pavlovic.