  In this work we prove that the solution of the Serre-Green-Naghdi equation
cannot be globally defined when the interface reaches the impervious bottom
tangentially. As a consequence, our result complements the paper \emph{Camassa,
R., Falqui, G., Ortenzi, G., Pedroni, M., \& Thomson, C. Hydrodynamic models
and confinement effects by horizontal boundaries. Journal of Nonlinear Science,
29(4), 1445-1498, 2019.} Furthermore, we also prove that the solution to the
$abcd-$Boussinesq system can change sign in finite time. Finally, we provide
with a proof of a scenario of finite time singularity for the $abcd-$Boussinesq
system. These latter mathematical results are related to the numerics in
\emph{Bona, \& Chen, Singular solutions of a Boussinesq system for water waves.
J. Math. Study, 49(3), 205-220, 2016}.
