Remarks on the well-posedness of Camassa-Holm type equations in Besov spaces

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• 作者：Jinlu Li^a ; ^{lijl29@mail2.sysu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Zhaoyang Yin^a ; ^b ; ^{mcsyzy@mail.sysu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Camassa&ndash ; Holm type equations ; Littlewood&ndash ; Paley theory ; The continuity of the solution map ; Nonhomogeneous Besov spaces
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 December 2016
• 年：2016
• 卷：261
• 期：11
• 页码：6125-6143
• 全文大小：350 K

文摘

In this paper, we prove the solution map of the Cauchy problem of Camassa–Holm type equations depends continuously on the initial data in nonhomogeneous Besov spaces in the sense of Hadamard by using the Littlewood–Paley theory and the method introduced by Kato [37] and Danchin [21].