The authors prove he existence of attractors for the 2d-Navier-Stokes equations with an exterior force by using the theory of processes by Babin, Vishik and others. A process is based on a Banach space , an index set (itself a topological vector space). A process is a collection of nonlinar operators, acting on , labeled by such that
is called the symbol space, a symbol. Concepts such as uniform attractor, uniform absorbing set etc. are now introduced. E.g., is uniformly absorbing if given and a bounded set there is such that
The authors now prove a number of preparatory lemmas concerning properties of processes. These results are then applied to the 2d-Navier-Stokes equation on a smooth bounded domain . To this end this equation is put into standard abstract form
based on the Hilbert spaces
The exterior force , is taken as symbol of the system (3), resp. of the induced process; one assumes
After recalling global existence and uniqueness of solutions of (3) the authors proceed to prove the existence of a uniform attractor of (3) and investigate its properties. The relevant Theorem 3.3 states among others (expressed somewhat losely) that if , has an additional property called “normal” then the associated with , coincides with the uniform attractor associated with , , for any . Further results of this type are obtained (Theorems 4.1, 4.2).