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 Hunterr-Saxton system. We also show for both systems that if singularities appear in finite time, they are necessary in the first derivatives.

Published in Nonlinear Anal. Real World Appl. in 2022

References in corpus (2)

• Global weak solutions of a Hamiltonian regularised Burgers equation
• On a Hamiltonian regularization of scalar conservation laws

Cited by in corpus (4)

• Global weak solutions of a Hamiltonian regularised Burgers equation
• Global weak solutions of the Serre-Green-Naghdi equations with surface tension
• On the blow-up scenario for some modified Serre-Green-Naghdi equations
• Local well-posedness of a Hamiltonian regularisation of the Saint-Venant system with uneven bottom