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Journal Articles Nonlinear Analysis: Real World Applications Year : 2022

Hamiltonian regularisation of the unidimensional barotropic Euler equations

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 Hunter-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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Dates and versions

hal-02907304 , version 1 (27-07-2020)

Identifiers

Cite

Billel Guelmame, Didier Clamond, Stéphane Junca. Hamiltonian regularisation of the unidimensional barotropic Euler equations. Nonlinear Analysis: Real World Applications, 2022, 64, 22p. ⟨10.1016/j.nonrwa.2021.103455⟩. ⟨hal-02907304⟩
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