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Non-uniform dependence on initial data for the 2D viscous shallow water equations by Li, Jinlu; Yu, Yanghai; Zhu, Weipeng is a scholarly article available to read on EtoBox.

What is Non-uniform dependence on initial data for the 2D viscous shallow water equations about?

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 $s>2$.

Author

Li, Jinlu; Yu, Yanghai; Zhu, Weipeng

Published

2020

Language

EN