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