  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 $B^1_{\infty,1}$.
