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

Abstract

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.

References in corpus (2)

• Global weak solutions of a Hamiltonian regularised Burgers equation
• Hamiltonian regularisation of the unidimensional barotropic Euler equations

Cited by in corpus (1)

• On a Hamiltonian regularization of scalar conservation laws