Abstract
In this paper, we consider the Cauchy problem for the two-component Fornberg–Whitham system on the real line and study the issue of uniform dependence on initial data for this equation. We prove that the solution map of this problem cannot be uniformly continuous in Sobolev spaces \(H^s({\mathbb {R}})\times H^{s-1}({\mathbb {R}})\) for \(s > {\frac{3}{2}}\).
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Acknowledgements
The authors would like to thank the anonymous referee for the valuable comments and suggestions which greatly improved the paper. Y. Yu is supported by the National Natural Science Foundation of China (12101011) and Natural Science Foundation of Anhui Province (1908085QA05). J. Li is supported by the National Natural Science Foundation of China (11801090 and 12161004) and Jiangxi Provincial Natural Science Foundation (20212BAB211004).
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Yu, Y., Li, J. Non-uniform dependence of the data-to-solution map for the two-component Fornberg–Whitham system. Annali di Matematica 202, 59–76 (2023). https://doi.org/10.1007/s10231-022-01232-8
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DOI: https://doi.org/10.1007/s10231-022-01232-8