Event Detail

Event Type: 
Department Colloquium
Date/Time: 
Monday, April 7, 2014 - 09:00 to 10:00
Location: 
Kidder 350

Speaker Info

Institution: 
Indiana University
Abstract: 

We discuss a variety of results regarding the global attractor of the 2D Navier-Stokes equations (NSE). This finite dimensional set contains all the long time behavior of the system, including steady states, limit cycles, unstable manifolds, and any solution bounded for all time. In fact, solutions in the global attractor extend to holomorphic functions for the NSE with a complexified time variable. There is a fixed strip about the real time axis on which uniform bounds in higher Sobolev-type norms hold, The reason for the title is an “all for one, one for all” law which states that if any element of the attractor is in a certain function class, then all of the attractor must be. This is tied to the question of whether the zero solution can be in the global attractor for a nonzero force, which in turn is related to cascade phenomenon of turbulence theory.