On the blow-up scenario for some modified Serre–Green–Naghdi equations. (November 2022) - Guelmame, Billel
Abstract: The present paper deals with a modified Serre–Green–Naghdi (mSGN) system that has been introduced by Clamond et al. (2017) to improve the dispersion relation. We present a precise blow-up scenario of the mSGN equations and we prove the existence of a class of solutions that develop singularities in finite time. All the presented results hold, with the same proof, for the Serre–Green–Naghdi system with surface tension.