Non-uniform continuous dependence on initial data of solutions to the Euler-Poincar\'{e} system
Analysis of PDEs
2020-01-08 v1
Abstract
In this paper, we investigate the continuous dependence on initial data of solutions to the Euler-Poincar\'{e} system. By constructing a sequence approximate solutions and calculating the error terms, we show that the data-to-solution map is not uniformly continuous in Sobolev space for .
Cite
@article{arxiv.1812.11182,
title = {Non-uniform continuous dependence on initial data of solutions to the Euler-Poincar\'{e} system},
author = {Jinlu Li and Li Dai and Weipeng Zhu},
journal= {arXiv preprint arXiv:1812.11182},
year = {2020}
}
Comments
10 pages. arXiv admin note: text overlap with arXiv:1505.00086 by other authors