Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation

By Zhaoyang Yin, O. Lechtenfeld, Joachim Escher. 2007

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Global Solutions for the Two-Component Camassa–Holm System (2011, methodology): “up property of the solutions and the continuity of the semigroup with respect to a new distance which is introduced. The vanishing density limit is not discussed in [25]. Escher, Lechtenfeld, and Yin [6] established a short-time existence theory for solutions using Kato techniques in the case η = −1”
On the global existence and wave-breaking criteria for the two-component Camassa-Holm system (2010, methodology): “For example, Escher, Lechtenfeld and Yin [18] investigated local wellposedness for the two-component Camassa–Holm system with initial data (u0, ρ0) ∈ Hs ×Hs−1 with s 2 and derived some precise blow-up scenarios for strong solutions to the system.”
On the Cauchy problem for the two-component Camassa–Holm system (2011, background): “A similar estimate can also be found in [20].”
Well-posedness and blow-up solution for a modified two-component periodic Camassa–Holm system with peakons (2010, unknown): “[7,18,25] and references therein.”