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global weak solutions

Proceedings of the Edinburgh Mathematical Society (1)

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On the existence of global weak solutions to an integrable two-component Camassa–Holm shallow-water system
Part of
- General higher-order equations and systems
- Hyperbolic equations and systems
Chunxia Guan, Zhaoyang Yin
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 56 / Issue 3 / October 2013

Published online by Cambridge University Press:

28 June 2013, pp. 755-775
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In this paper, we investigate the existence of global weak solutions to an integrable two-component Camassa–Holm shallow-water system, provided the initial data u0(x) and ρ0(x) have end states u± and ρ±, respectively. By perturbing the Cauchy problem of the system around rarefaction waves of the well-known Burgers equation, we obtain a global weak solution for the system under the assumptions u− ≤ u+ and ρ− ≤ ρ+.