Non-uniform dependence on initial data for the Camassa-Holm equation in Besov spaces

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Li, Jinlu¹  Yu, Yanghai²  Zhu, Weipeng³ 

[1] Gannan Normal Univ, Sch Math & Comp Sci, Ganzhou 341000, Peoples R China

[2] Anhui Normal Univ, Sch Math & Stat, Wuhu 241000, Anhui, Peoples R China

[3] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Peoples R China

关键词: Camassa-Holm equation;    Non-uniform continuous dependence;    Besov spaces;   

DOI  :  10.1016/j.jde.2020.06.028

来源: Elsevier

【 摘 要 】

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. This result improves considerably the previous work given by Himonas-Kenig [23]. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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