Uniqueness of Conservative Solutions to the Camassa-Holm Equation via Characteristics
By Alberto Bressan, Geng Chen, Qingtian Zhang. 2014
105 citations recorded by the source corpus.
The paper provides a direct proof the uniqueness of solutions to the Camassa-Holm equation, based on characteristics. Given a conservative solution u = u(t,x), an equation is introduced which singles out a unique characteristic curve through each initial point. By studying the evolution of the quantities u and v = 2arctanux along each characteristic, it is proved that the Cauchy problem with general initial data u0 ∈ H 1 (IR) has a unique solution, globally in time.
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/28c141dcec867c719ce765cd8377cfd42deae7f7
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In Geometry and Topology
- Qingtian Zhang
- Geng Chen
- Alberto Bressan
- Helge Holden
- Xavier Raynaud
- Yue Liu
- Zhaoyang Yin
- A. Alexandrou Himonas
In Mathematical Physics
- Geng Chen
- Alberto Bressan
- Qingtian Zhang
- Luigi Ambrosio
- Gianluca Crippa
- Camillo De Lellis
- Stefano Bianchini
- J. Ball
In Statistical and Nonlinear Physics
- Geng Chen
- Qingtian Zhang
- Alberto Bressan
- Helge Holden
- Xavier Raynaud
- Yue Liu
- Zhaoyang Yin
- Adrian Constantin
Citations in the corpus
- Unique Conservative Solutions to a Variational Wave Equation (2014, methodology): “The main technique used in the proof is similar to the paper [3] by the same authors, dealing with the Camassa–Holm equation, and was inspired by the uniqueness result in [9].”