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Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation. (English) Zbl 1149.35307

Authors’ abstract: After some remarks on a possible zero-curvature formulation we first establish local well-posedness for the 2-component Camassa-Holm equation. Then precise blow-up scenarios for strong solutions to the system are derived. Finally we present two blow-up results for strong solutions to the system.

MSC:

35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35G25 Initial value problems for nonlinear higher-order PDEs
35Q35 PDEs in connection with fluid mechanics
35B40 Asymptotic behavior of solutions to PDEs
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