Non-uniform continuous dependence on initial data of solutions to the Euler-Poincaré system

Abstract

In this paper, we investigate the continuous dependence on initial data of solutions to the Euler-Poincaré 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 $H^s({\mathbb{R}}^d)$ for $s>1+\frac{d}{2}$.

10 pages. arXiv admin note: text overlap with arXiv:1505.00086 by other authors