On the blow-up scenario for some modified Serre–Green–Naghdi equations. (November 2022)

• Record Type: Journal Article
• Authors: Guelmame, Billel
• Is Part Of: Nonlinear analysis. Volume 224(2022)
• Publication Date: 2022-11
• Subjects: 35Q35 -- 35B65 -- 35B44 -- 76B15; Serre–Green–Naghdi -- Dispersion -- Water waves -- Energy conservation -- Blow-up -- Shallow water; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.113084
• Languages: English
• ISSNs: 0362-546X

Abstract

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.