Persistence of the solution to the Euler equations in the end-point critical Triebel-Lizorkin space $F_{1,\mathrm{\infty }}^{d+1}({\mathbb{R}}^d)$

Local stay of the solutions to the Euler equations for an ideal incompressible fluid in the end-point Triebel-Lizorkin spaces $F_{1,\mathrm{\infty }}^s({\mathbb{R}}^d)$ with $s\ge d+1$ is clarified.