Global attractors for small samples and germs of 3D Navier-Stokes equations

We prove the existence of a global attractor for the generalized semiflow (in the sense of J.M. Ball) on the space of small samples of solutions to the 3D incompressible Navier-Stokes equations. This way to overcome the possible nonuniqueness of solutions is less radical than that of G. Sell and does not provide unique solutions. On the other hand, the existence of the global attractor does not need the unproven hypothesis of continuity of solutions required by Ball. The extension of this approach to the space of germs of solutions is also discussed. (c) 2005 Elsevier Ltd. All rights reserved.