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