Non-uniform dependence for the two-component Camassa-Holm shallow water system (2010.08747v1)

Published 17 Oct 2020 in math.AP

Abstract: In this paper, we consider the solution map of the initial value problem to the two-component Camassa-Holm equation on the line. We prove that the solution map of this problem is not uniformly continuous in Sobolev spaces $H^s(\R)\times H^{s-1}(\R)$ for $s>3/2$.

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