🚀 go-pugleaf

In article <1992Jul20.153122.29180@murdoch.acc.Virginia.EDU> crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass) writes:
>In article <1076@kepler1.rentec.com> andrew@rentec.com (Andrew Mullhaupt) writes:
>>OK but there is still a universal attractor for the N-S equations as
>>rigorously proved by Foias et. al. The dimension is about 500 (as one
>>expects from various other estimates). Renormalization is not necessary
>>for an attractor, although the Orszag-Yahot theory is essentially a
>>renormalization theory. The Foias stuff can be found in the book by
>>Foias and Constantine, but I think the attractor theorems came after
>>his book with Roger Temam, although my memory may be playing tricks.

>     Is this the 'universal attractor' for 2-D NS with periodic and
>     dirichlet BC's?  

Could someone elaborate a bit more on this idea and what precisely was
proved?  I find it rather odd.  I seem to recall that the 2-D nonlinear
Schrodinger equation with cubic nonlinearity is completely integrable
(let's take periodic boundary conditions, say).  What sort of
nonlinearities does Foias consider, and what is a "universal attractor"?