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 Anal. Non Linéaire 41 (2024), no. 3, pp. 749–795

DOI 10.4171/AIHPC/99