Finite time blow-up for a dyadic model of the Euler equations

Natasa Pavlovic University of Illinois at Chicago

This talk will be about joint work with Nets Katz on dyadic models for the equations of fluid motion. We introduce a dyadic model for the Euler and the Navier-Stokes equations. The dyadic model possesses an important feature of the equations, which is conservation (or decay) of energy. For the dyadic Euler equations we prove finite time blow-up. In the context of the dyadic Navier-Stokes equations with hyper-dissipation we prove finite time blow-up in case when the dissipation degree is sufficiently small.