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On solutions to a two-component generalized Camassa-Holm equation. (English) Zbl 1189.35255
Summary: We consider a two-component Camassa-Holm system which arises in shallow water theory. We analyze a wave breaking mechanism and the global existence of solutions. First, we discuss the local well posedness and a blow up mechanism, then establish some new blow up criteria for this system formulated either on the line or with space-periodic initial conditions. Finally, the existence of global solutions is analyzed.
35Q35PDEs in connection with fluid mechanics
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B03Existence, uniqueness, and regularity theory (fluid mechanics)
76T99Two-phase and multiphase flows
35B44Blow-up (PDE)
37N10Dynamical systems in fluid mechanics, oceanography and meteorology