Non-uniform dependence on initial data for the Camassa-Holm equation in Besov spaces
Analysis of PDEs
2020-01-07 v2
Abstract
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}.
Keywords
Cite
@article{arxiv.2001.00290,
title = {Non-uniform dependence on initial data for the Camassa-Holm equation in Besov spaces},
author = {Jinlu Li and Yanghai Yu and Weipeng Zhu},
journal= {arXiv preprint arXiv:2001.00290},
year = {2020}
}