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arXiv · 2403.02208

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

Billel Guelmame
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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.

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Billel Guelmame. 2024-03-04. On the blow-up scenario for some modified Serre-Green-Naghdi equations. https://doi.org/10.1016/j.na.2022.113084

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