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NON-UNIFORM DEPENDENCE ON INITIAL DATA FOR THE FORNBERG-WHITHAM EQUATION IN C1(ℝ)

  • Yanghai Yu (School of Mathematics and Statistics Anhui Normal University)
  • Received : 2023.08.24
  • Accepted : 2024.01.26
  • Published : 2024.05.31
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Abstract

It is shown in [1] that the Cauchy problem for the Fornberg-Whitham equation is well-posed in C1(ℝ) and the data-to-solution map is Hölder continuous from Cα to C([0, T]; Cα) with α ∈ [0, 1). In this short paper, we further show that the data-to-solution map of the Fornberg-Whitham equation is not uniformly continuous on the initial data in C1(ℝ).

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Acknowledgement

The author would like to thank the anonymous referees for valuable comments and suggestions which greatly improved the presentation of this paper and also thank Dr. Jinlu Li for helpful comments on a preliminary version of this work. Y. Yu is supported by National Natural Science Foundation of China (12101011).

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