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Journal Articles Annales de l'Institut Henri Poincaré C, Analyse non linéaire Year : 2023

Global weak solutions of the Serre–Green–Naghdi equations with surface tension

Abstract

We consider in this paper the Serre--Green--Naghdi equations with surface tension. Smooth solutions of this system conserve an $H^1$-equivalent energy.We prove the existence of global weak dissipative solutions for any relatively small-energy initial data.We also prove that the Riemann invariants of the solutions satisfy a one-sided Oleinik inequality.
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Dates and versions

hal-03585433 , version 1 (23-02-2022)
hal-03585433 , version 2 (03-04-2023)

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Billel Guelmame. Global weak solutions of the Serre–Green–Naghdi equations with surface tension. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, In press, ⟨10.4171/aihpc/99⟩. ⟨hal-03585433v2⟩
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