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arXiv · 2403.02214

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

Billel Guelmame
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Abstract

We consider in this paper the Serre--Green--Naghdi equations with surface tension. Smooth solutions of this system conserve an $H^1$-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.

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Billel Guelmame. 2024-03-04. Global weak solutions of the Serre-Green-Naghdi equations with surface tension. https://doi.org/10.4171/aihpc%2F99

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