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arXiv · 1812.11182

Non-uniform continuous dependence on initial data of solutions to the Euler-Poincar\'{e} system

Jinlu Li·Li Dai·Weipeng Zhu
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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 $H^s(\mathbb{R}^d)$ for $s>1+\frac d2$.

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Jinlu Li, Li Dai, Weipeng Zhu. 2018-12-30. Non-uniform continuous dependence on initial data of solutions to the Euler-Poincar\'{e} system. https://doi.org/10.1063/1.5097914

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