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Analysis on continuity of the solution map for the Whitham equation in Besov spaces

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  • Zhengyan Liu
  • Xinglong Wu

Abstract

This paper is devoted to studying the continuity of the solution map for the Cauchy problem of the Whitham equation. First, the continuity dependence of solution is established in B2,rs$\mathrm{B}^{s}_{2,r}$ in the sense of Hadamard. Next, by constructing approximate solutions, we show that the data‐to‐solution map is not uniformly continuous in Besov spaces B2,rs$\mathrm{B}^{s}_{2,r}$ (s>32,1≤r≤∞$s>\frac{3}{2}, 1\le r\le \infty$) on the periodic case and on the line. The crucial technical tool used to prove this result is Lemma 5.1, which generalizes the result of Lemma 3 in [23].

Suggested Citation

  • Zhengyan Liu & Xinglong Wu, 2024. "Analysis on continuity of the solution map for the Whitham equation in Besov spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 297(4), pages 1451-1467, April.
    • Handle: RePEc:bla:mathna:v:297:y:2024:i:4:p:1451-1467
    DOI: 10.1002/mana.202300132
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