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arXiv · 1611.05894

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

John Holmes·Barbara Lee Keyfitz·Feride Tiglay
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Abstract

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.

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John Holmes, Barbara Lee Keyfitz, Feride Tiglay. 2016-11-17. Nonuniform dependence on initial data for compressible gas dynamics: The Cauchy problem on $\mathbb{R}^2$. https://arxiv.org/abs/1611.05894

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