TITLE:
Blow-Up for a Periodic Two-Component Camassa-Holm Equation with Generalized Weakly Dissipation
AUTHORS:
Yang Li, Jingyi Liu, Xincheng Zhu
KEYWORDS:
Periodic Two-Component Camassa-Holm Equation, Local Well-Posedness, Blow-Up, Global Existence, Monotonicity
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.8 No.10,
October
28,
2020
ABSTRACT: In this paper we study a periodic two-component Camassa-Holm equation with generalized weakly dissipation. The local well-posedness of Cauchy problem is investigated by utilizing Kato’s theorem. The blow-up criteria and the blow-up rate are established by applying monotonicity. Finally, the global existence results for solutions to the Cauchy problem of equation are proved by structuring functions.