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 [6, 7, 9]. The proof relies on the classical Bona–Smith method as [12], where similar result was obtained in critical Besov spaces $$B^1_{\infty ,1}$$ .