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Non-uniform continuous dependence on initial data of solutions to the Euler-Poincaré system (1812.11182v1)
Published 30 Dec 2018 in math.AP
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 $Hs(\mathbb{R}d)$ for $s>1+\frac d2$.
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