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arXiv · 2011.14125

Non-uniform dependence on initial data for the 2D viscous shallow water equations

Jinlu Li·Yanghai Yu·Weipeng Zhu
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Abstract

The failure of uniform dependence on the data is an interesting property of classical solution for a hyperbolic system. In this paper, we consider the solution map of the Cauchy problem to the 2D viscous shallow water equations which is a hyperbolic-parabolic system. We prove that the solution map of this problem is not uniformly continuous in Sobolev spaces $H^s\times H^{s}$ for $s>2$.

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Jinlu Li, Yanghai Yu, Weipeng Zhu. 2020-11-28. Non-uniform dependence on initial data for the 2D viscous shallow water equations. https://arxiv.org/abs/2011.14125

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