Author(s)

Yang Li^*, Jingyi Liu, Xincheng Zhu

Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang, China.

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.

Periodic Two-Component Camassa-Holm Equation, Local Well-Posedness, Blow-Up, Global Existence, Monotonicity

Li, Y. , Liu, J. and Zhu, X. (2020) Blow-Up for a Periodic Two-Component Camassa-Holm Equation with Generalized Weakly Dissipation. Journal of Applied Mathematics and Physics, 8, 2223-2240. doi: 10.4236/jamp.2020.810167.