English

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 Hs(Rd)H^s(\mathbb{R}^d) for s>1+d2s>1+\frac d2.

Keywords

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

R2 v1 2026-06-23T06:58:21.684Z