We prove the continuous dependence of the solution maps for the Euler equations in the (critical) Triebel–Lizorkin spaces, which was not shown in the previous works [6, 7, 9]. The proof relies on the classical Bona–Smith method as [12], where similar result was obtained in critical Besov spaces \(B^1_{\infty ,1}\).

中文翻译：

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关于Triebel–Lizorkin空间中Euler方程的正定性的说明

我们证明了（临界）Tr​​iebel–Lizorkin空间中Euler方程解映射的连续依赖性，这在以前的工作中没有显示[6，7，9]。该证明依赖于经典的Bona–Smith方法[12]，其中在临界Besov空间\（B ^ 1 _ {\ infty，1} \）中获得了相似的结果。