Blow-up phenomenon, ill-posedness and peakon solutions for the periodic Euler-Poincar\'e equations
Analysis of PDEs
2018-10-19 v1
Abstract
In this paper we mainly investigate the initial value problem of the periodic Euler-Poincar\'e equations. We first present a new blow-up result to the system for a special class of smooth initial data by using the rotational invariant properties of the system. Then, we prove that the periodic Euler-Poincar\'e equations is ill-posed in critical Besov spaces by a contradiction argument. Finally, we verify the system possesses a class of peakon solutions in the sense of distributions.
Keywords
Cite
@article{arxiv.1810.07993,
title = {Blow-up phenomenon, ill-posedness and peakon solutions for the periodic Euler-Poincar\'e equations},
author = {Wei Luo and Zhaoyang Yin},
journal= {arXiv preprint arXiv:1810.07993},
year = {2018}
}