The authors give several very interesting results on the determination of the solutions of the Navier-Stokes equations of incompressible viscous fluids by their values on a finite set. For instance, two stationary solutions in a bounded domain of , coincide if they coincide on a finite set sufficiently dense.
In the 2-dimensional case, let f,g be two body forces such that f(t)- g(t) in , as . Then if the corresponding strong solutions u and v are such that in as , for every of a finite set, sufficiently dense, then u( in C().
A similar statement holds for time-periodic solutions. The large time behaviour of the solution is therefore determined by its large time behaviour on a suitable discrete set.