  In this note, using the ideas from our recent article \cite{EM}, we prove
strong ill-posedness for the 2D Euler equations in $C^k$ spaces. This note
provides a significantly shorter proof of many of the main results in
\cite{BLi2}. In the case $k>1$ we show the existence of initial data for which
the $kth$ derivative of the velocity field develops a logarithmic singularity
immediately. The strong ill-posedness covers $C^{k-1,1}$ spaces as well. The
ill-posedness comes from the pressure term in the Euler equation. We formulate
the equation for $D^k u$ as:
  $$\partial_t D^k u=D^{k+1} p + l.o.t.$$
  and then use the non-locality of the map $u\rightarrow p$ to get the
ill-posedness. The real difficulty comes in how to deal with the "l.o.t." terms
which can be handled by special commutator estimates.
