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Non-uniform continuity of the Fokas–Olver–Rosenau–Qiao equation in Besov spaces

Abstract

In this paper, we consider the solution map of the Cauchy problem to the Fokas–Olver–Rosenau–Qiao equation on the real line and prove that the solution map of this problem is not uniformly continuous on the initial data in Besov spaces. Our result extends the previous results in Himonas and Mantzavinos (Nonlinear Anal 95:499–529, 2014) and Li et al. (J Math Fluid Mech 22:50, 2020).

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Acknowledgements

The authors want to thank the referees for their careful reading and helpful suggestions, which greatly improved the presentation of this paper. The authors are very grateful to Dr. Jinlu Li for some useful suggestions. Y. Yu is supported by the Natural Science Foundation of Anhui Province (No. 1908085QA05). This work is partially supported by the National Natural Science Foundation of China (Grant No. 11801090).

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Correspondence to Xing Wu.

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Wu, X., Yu, Y. Non-uniform continuity of the Fokas–Olver–Rosenau–Qiao equation in Besov spaces. Monatsh Math (2021). https://doi.org/10.1007/s00605-021-01637-2

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Keywords

  • Fokas–Olver–Rosenau–Qiao equation
  • Non-uniform continuous dependence
  • Besov spaces

Mathematics Subject Classification

  • 35B30
  • 35G25
  • 35Q53