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- Publisher
- Springer Journals
- Copyright
- Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
- Subject
- Mathematics; Analysis
- ISSN
- 1424-3199
- eISSN
- 1424-3202
- DOI
- 10.1007/s00028-018-0430-x
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, we consider the uniqueness of global-in-time conservative weak solutions for the modified two-component Camassa–Holm system on real line. The strategy of proof is based on characteristics. Given a conservative weak solution, an equation is introduced to single out a unique characteristic curve through each initial point coordinate transformation into the Lagrangian coordinates. We prove that the Cauchy problem of the modified two-component Camassa–Holm system with initial data $$z_0=(u_0,\gamma _0)\in H^1(\mathbb {R})\times (H^1(\mathbb {R})\cap W^{1,\infty }(\mathbb {R}))$$ z 0 = ( u 0 , γ 0 ) ∈ H 1 ( R ) × ( H 1 ( R ) ∩ W 1 , ∞ ( R ) ) has a unique global conservative weak solution.
Journal
Journal of Evolution Equations – Springer Journals
Published: Feb 23, 2018