The Cauchy problem for fractional Camassa–Holm equation in Besov space. (October 2021)

• Record Type: Journal Article
• Authors: Fan, Lili; Gao, Hongjun; Wang, Junfang; Yan, Wei
• Is Part Of: Nonlinear analysis. Volume 61(2021)
• Publication Date: 2021-10
• Subjects: Besov spaces -- Fractional Camassa–Holm equation -- Local well-posedness -- Blow-up criterion -- Analyticity; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103348
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we consider the fractional Camassa–Holm equation modeling the propagation of small-but-finite amplitude long unidirectional waves in a nonlocally and nonlinearly elastic medium. First, we establish the local well-posedness in Besov space B 2, 1 s 0 with s 0 = 2 ν − 1 2 for ν > 3 2 and s 0 = 5 2 for 1 < ν ≤ 3 2 . Then, with a given analytic initial data, we establish the analyticity of the solutions in both variables, globally in space and locally in time. Finally, we give a blow-up criterion.