English

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 H1H^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.

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}
}