  The aim of the current paper is to illustrate, in a simple example, our
recent, very general, rigorous results [Bru J.-B., de Siqueira Pedra W., J.
Math. Anal. Appl. (2020), doi.org: 10.1016/j.jmaa.2020.124434 and
10.1016/j.jmaa.2020.124517] on the dynamical properties of fermions and
quantum-spin systems with long-range, or mean-field, interactions, in infinite
volume. We consider here the strong-coupling BCS-Hubbard model, because this
example is very pedagogical and, at the same time, physically relevant for it
highlights the impact of the (screened) Coulomb repulsion on ($s$-wave)
superconductivity.
