Weak well-posedness for a modified two-component Camassa–Holm system. (January 2019)

• Record Type: Journal Article
• Authors: Guan, Chunxia; Wang, Jianming; Meng, Yiping
• Is Part Of: Nonlinear analysis. Volume 178(2019)
• Page Start: 247
• Page End: 265
• Publication Date: 2019-01
• Subjects: 35B30 -- 35G55 -- 35Q35 -- 35Q53; Modified two-component Camassa–Holm system -- Weak well-posedness -- Characteristics; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.07.019
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we consider the weak well-posedness for a modified two-component Camassa–Holm system with initial data z 0 = ( u 0, γ 0 ) ∈ ( H 1 ( R ) ∩ W 1, ∞ ( R ) ) × ( H 1 ( R ) ∩ W 1, ∞ ( R ) ) . At first, by introducing a new set of independent variables, we transform the modified two-component Camassa–Holm system into an ODE system. Then, we prove the local existence and uniqueness of the solution to the ODE system and obtain the unique solution to the original system. Finally, we investigate the weak continuous dependence on initial conditions to the modified two-component Camassa–Holm system.