Local well-posedness in the critical Besov space and blow-up for an n-component Camassa–Holm system

• Published in: Journal of mathematical analysis and applications Vol. 504; no. 2; p. 125423
• Main Authors: Cheng, Wenguang, Xu, Tianzhou
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15-12-2021
• Subjects: Blow-up; Critical Besov space; Local well-posedness; N-component Camassa–Holm system; Local well-posedness; Critical Besov space; N-component Camassa–Holm system; Blow-up
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2021.125423

In this paper, the Cauchy problem of an n-component Camassa–Holm system is considered. The local well-posedness in the critical Besov space (B2,132)n is established, and it is shown that the data-to-solution map is Hölder continuous. We finally give two new blow-up conditions for the initial data to this system by virtue of the H1-norm conservation law.