  In the Reduced Basis approximation of Stokes and Navier-Stokes problems, the
Galerkin projection on the reduced spaces does not necessarily preserved the
inf-sup stability even if the snapshots were generated through a stable full
order method. Therefore, in this work we aim at building a stabilized Reduced
Basis (RB) method for the approximation of unsteady Stokes and Navier-Stokes
problems in parametric reduced order settings. This work extends the results
presented for parametrized steady Stokes and Navier-Stokes problems in a work
of ours \cite{Ali2018}. We apply classical residual-based stabilization
techniques for finite element methods in full order, and then the RB method is
introduced as Galerkin projection onto RB space. We compare this approach with
supremizer enrichment options through several numerical experiments. We are
interested to (numerically) guarantee the parametrized reduced inf-sup
condition and to reduce the online computational costs.
