On the blow-up scenario for some modified Serre–Green–Naghdi equations

Billel Guelmame (1, 2)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 COFFEE - COmplex Flows For Energy and Environment

The present paper deals with a modified Serre–Green–Naghdi (mSGN) system that has been introduced by Clamond et al. 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 also for the Serre–Green–Naghdi system with weak surface tension.

Mots clés: Serre–Green–Naghdi; dispersion; water waves; energy conservation; blow-up; shallow water

Domaines: Equations aux dérivées partielles [math.AP]

Billel Guelmame. On the blow-up scenario for some modified Serre–Green–Naghdi equations. Nonlinear Analysis: Theory, Methods and Applications, 2022, ⟨10.1016/j.na.2022.113084⟩. ⟨hal-03264688v2⟩