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.

References in corpus (1)

• Hamiltonian regularisation of the unidimensional barotropic Euler equations

Cited by in corpus (1)

• On a Hamiltonian regularization of scalar conservation laws