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The Cauchy problem for the two dimensional compressible Euler equations withdata in the Sobolev space $H^s(\mathbb R^2)$ is known to have a unique solutionof the same Sobolev class for a short time, and the data-to-solution map iscontinuous. We prove that the data-to-solution map on the plane is notuniformly continuous on any bounded subset of Sobolev class functions.

Nonuniform dependence on initial data for compressible gas dynamics: The Cauchy problem on $\mathbb{R}^2$