Global weak solutions of the Serre-Green-Naghdi equations with surface tension
Analysis of PDEs
2024-03-05 v1
Abstract
We consider in this paper 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.
Keywords
Cite
@article{arxiv.2403.02214,
title = {Global weak solutions of the Serre-Green-Naghdi equations with surface tension},
author = {Billel Guelmame},
journal= {arXiv preprint arXiv:2403.02214},
year = {2024}
}