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On the global existence and wave-breaking criteria for the two-component Camassa-Holm system. (English) Zbl 1189.35254
Summary: Considered herein is a two-component Camassa-Holm system modeling shallow water waves moving over a linear shear flow. A wave-breaking criterion for strong solutions is determined in the lowest Sobolev space H s ,s>3 2 by using the localization analysis in the transport equation theory. Moreover, an improved result of global solutions with only a nonzero initial profile of the free surface component of the system is established in this Sobolev space H s .
MSC:
35Q35PDEs in connection with fluid mechanics
35R37Moving boundary problems for PDE
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B03Existence, uniqueness, and regularity theory (fluid mechanics)
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