English

Two-component system modelling shallow-water waves with constant vorticity under the Camassa-Holm scaling

Analysis of PDEs 2024-06-14 v1

Abstract

This paper is concerned with the derivation of a two-component system modelling shallow-water waves with constant vorticity under the Camassa-Holm scaling from our newly established Green-Naghdi equations with a linear shear. It is worth pointing out that the ρ\rho component in this new system is quite different from the previous two-component system due to the effects of both vorticity and larger amplitude. We then establish the local well-posedness of this new system in Besov spaces, and present a blow-up criterion. We finally give a sufficient condition for global strong solutions to the system in some special case.

Keywords

Cite

@article{arxiv.2406.08874,
  title  = {Two-component system modelling shallow-water waves with constant vorticity under the Camassa-Holm scaling},
  author = {Leyi Zhang and Xingxing Liu},
  journal= {arXiv preprint arXiv:2406.08874},
  year   = {2024}
}