  We present a rigorous convergence result for the smooth solutions to a
singular semilinear hyperbolic approximation, a vector BGK model, to the
solutions to the incompressible Navier-Stokes equations in Sobolev spaces. Our
proof is based on the use of a constant right symmetrizer, weighted with
respect to the parameter of the singular pertubation system. This symmetrizer
provides a conservative-dissipative form for the system and this allow us to
perform uniform energy estimates and to get the convergence by compactness.
