Journal of Guangdong University of Technology ›› 2020, Vol. 37 ›› Issue (02): 80-86.doi: 10.12052/gdutxb.190053

• Comprehensive Studies • Previous Articles     Next Articles

Weak Well-posedness for the Generalized Camassa-Holm Equation

Chen Rong-ning, Wei Xue-mei   

  1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou, 510520, China
  • Received:2019-04-10 Online:2020-03-10 Published:2020-02-12

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Abstract: The weak well-posedness for the generalized Camassa-Holm equation with initial data u0 ∈ H1(R)∩W1,∞(R) is mainly considered. First, by introducing the characteristics, the generalized Camassa-Holm equation is transformed into an ODE(Ordinary Differential Equation)-similar equation. Then applying the ODE theory, the local existence and uniqueness of the solution to the new equation are proved. Finally, by using the relationship between the new equation and the original equation, the local existence and uniqueness of the solution are investigated, deriving the conclusion of the weak continuous dependence on initial data for the original equation.

Key words: Generalized Camassa-Holm equation, characteristics, weak continuous dependence

CLC Number: 

  • O175
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