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

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 $s>1+\frac d2$.

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