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Zbl 1228.35092
Gui, Guilong; Liu, Yue
On the Cauchy problem for the two-component Camassa-Holm system. (English)
[J] Math. Z. 268, No. 1-2, 45-66 (2011). ISSN 0025-5874; ISSN 1432-1823/e

The authors consider a two-component Camassa-Holm system, which includes the Camassa-Holm equation itself as a special case. This system is known to be integrable and to have a physical interpretation. They consider the question of existence and uniqueness for the initial value problem of this system. They also investigate whether or not this system admits wave-breaking phenomena similar to that of the Camassa-Holm equation itself. The authors claim to improve previously-known results for the system.
[Andrew Pickering (Madrid)]

MSC 2000:: *35G25 Initial value problems for nonlinear higher-order PDE
35L15 Second order hyperbolic equations, initial value problems
35B44

Keywords: Besov spaces; blow-up; local well-posedness; two-component Camassa-Holm system; wave-breaking

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