Singularity formation for the Serre-Green-Naghdi equations and applications to abcd-Boussinesq systems

  title={Singularity formation for the Serre-Green-Naghdi equations and applications to abcd-Boussinesq systems},
  author={Hantaek Bae and Rafael Granero-Belinch'on},
  journal={Monatshefte f{\"u}r Mathematik},
In this work we prove the existence of singularities in finite time for the Serre-Green-Naghdi equation 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… 
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