Non-uniform dependence on initial data for the Camassa-Holm equation in Besov spaces

By Jinlu Li, Yanghai Yu, Weipeng Zhu. Journal of Differential Equations, 2020

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In the paper, we consider the initial value problem to the Camassa-Holm equation in the real-line case. Based on the local well-posedness result and the lifespan, we proved that the data-to-solution map of this problem is not uniformly continuous in nonhomogeneous Besov spaces in the sense of Hadamard. Our obtained result improves considerably the result in \cite{H-K}.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/34b520f78d14e2e5464d2f3705ca888e0831e0dc