Global existence and blow-up for the Euler-Poincar\'{e} equations with a class of initial data
Analysis of PDEs
2024-05-03 v1
Abstract
In this paper we investigate the Cauchy problem of d-dimensional Euler-Poincar\'{e} equations. By choosing a class of new and special initial data, we can transform this d-dimensional Euler-Poincar\'{e} equations into the Camassa-Holm type equation in the real line. We first obtain some global existence results and then present a new blow-up result to the system under some different assumptions on this special class of initial data.
Cite
@article{arxiv.2405.01252,
title = {Global existence and blow-up for the Euler-Poincar\'{e} equations with a class of initial data},
author = {Jinlu Li and Yanghai Yu and Weipeng Zhu},
journal= {arXiv preprint arXiv:2405.01252},
year = {2024}
}