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

  • Billel Guelmame

    Université Côte d’Azur, Nice, France
Global weak solutions of the Serre–Green–Naghdi equations with surface tension cover

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Abstract

In this paper we consider the Serre–Green–Naghdi equations with surface tension. Smooth solutions of this system conserve an -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.

Cite this article

Billel Guelmame, Global weak solutions of the Serre–Green–Naghdi equations with surface tension. Ann. Inst. H. Poincaré C Anal. Non Linéaire (2023), published online first

DOI 10.4171/AIHPC/99