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arXiv · 2402.15261

Hamiltonian regularisation of the unidimensional barotropic Euler equations

Billel Guelmame·Didier Clamond·Stéphane Junca
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Abstract

Recently, a Hamiltonian regularised shallow water (Saint-Venant) system has been introduced by Clamond and Dutykh. This system is Galilean invariant, linearly non-dispersive and conserves formally an $H^1$-like energy. In this paper, we generalise this regularisation for the barotropic Euler system preserving the same properties. We prove the local (in time) well-posedness of the regularised barotropic Euler system and a periodic generalised two-component Hunterr-Saxton system. We also show for both systems that if singularities appear in finite time, they are necessary in the first derivatives.

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Billel Guelmame, Didier Clamond, Stéphane Junca. 2024-02-23. Hamiltonian regularisation of the unidimensional barotropic Euler equations. https://doi.org/10.1016/j.nonrwa.2021.103455

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