  The Cauchy problem for the two dimensional compressible Euler equations with
data in the Sobolev space $H^s(\mathbb R^2)$ is known to have a unique solution
of the same Sobolev class for a short time, and the data-to-solution map is
continuous. We prove that the data-to-solution map on the plane is not
uniformly continuous on any bounded subset of Sobolev class functions.
