Remarks on the well-posedness of the Euler equations in the Triebel-Lizorkin spaces

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(\cite{Ch02, Ch03, ChMiZh10}). The proof relies on the classical Bona-Smith method as \cite{GuLiYi18}, where similar result was obtained in critical Besov spaces $B_{\mathrm{\infty },1}^1$.