Stability of blow-up solution for the two component Camassa–Holm equations

Article type: Research Article

Authors: Li, Xintao^a | Huang, Shoujun^b | Yan, Weiping^{a; *}

Affiliations: [a] School of Mathematics, Xiamen University, Xiamen, P.R. China. E-mail: yanwp@xmu.edu.cn | [b] School of Mathematics and Computer Science, Anhui Normal University, Wuhu, P.R. China. E-mail: sjhuang@mail.ahnu.edu.cn

Correspondence: [*] Corresponding author. E-mail: yanwp@xmu.edu.cn.

Abstract: This paper studies the wave-breaking mechanism and dynamical behavior of solutions near the explicit self-similar singularity for the two component Camassa–Holm equations, which can be regarded as a model for shallow water dynamics and arising from the approximation of the Hamiltonian for Euler’s equation in the shallow water regime.

Keywords: Camassa–Holm equation, blow-up solution, asymptotic analysis, stability

DOI: 10.3233/ASY-191590

Journal: Asymptotic Analysis, vol. 120, no. 3-4, pp. 319-336, 2020