Local well-posedness of a Hamiltonian regularisation of the Saint-Venant system with uneven bottom

Abstract

We prove in this note the local (in time) well-posedness of a broad class of $2\times 2$ symmetrisable hyperbolic system involving additional non-local terms. The latest result implies the local well-posedness of the non dispersive regularisation of the Saint-Venant system with uneven bottom introduced by Clamond, Dutykh and Mitsotakis. We also prove that, as long as the first derivatives are bounded, singularities cannot appear.

Published in Methods and Applications of Analysis in 2022

References in corpus (2)

• Hamiltonian regularisation of the unidimensional barotropic Euler equations
• On a Hamiltonian regularization of scalar conservation laws