Dyadic models for the equations of fluid motion

Natasa Pavlovic,  Institute for Advanced Studies

 

Abstract: In this talk we shall introduce a scalar dyadic model for the Euler and the Navier-Stokes equations in three dimensions and will discuss some of the results that were obtained for these models. For the dyadic Euler equations we prove finite time blow-up, while in the context of the dyadic Navier-Stokes equations with hyper-dissipation we prove finite time blow-up in case when the degree of dissipation is sufficiently small (joint work with Nets Katz). These results can be generalized to analogous results for a vector dyadic model (joint work with Susan Friedlander). Recently we analyzed a long time behavior of solutions to the dyadic Navier-Stokes equations in a critical space (joint work with James Colliander, Carlos Kenig and Gigliola Staffilani). Also time permitting, we shall mention some results for the dyadic equations that could be turned into results for the actual Navier-Stokes equations.