  We prove that the 2D Euler equations are not locally well-posed in $C^1$. Our
approach relies on the technique of Lagrangian deformations and norm inflation
of Bourgain and Li. We show that the assumption that the data-to-solution map
is continuous in $C^1$ leads to a contradiction with a well-posedness result in
$W^{1,p}$ of Kato and Ponce.
