  A hyperbolic relaxation of the classical Navier-Stokes problem in 2D bounded
domain with Dirichlet boundary conditions is considered. It is proved that this
relaxed problem possesses a global strong solution if the relaxation parameter
is small and the appropriate norm of the initial data is not very large.
Moreover, the dissipativity of such solutions is established and the singular
limit as the relaxation parameter tends to zero is studied
