Global Existence for the Generalized Two-Component Hunter–Saxton System
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- Wu, H. & Wunsch, M. J. Math. Fluid Mech. (2012) 14: 455. doi:10.1007/s00021-011-0075-9
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We study the global existence of solutions to a two-component generalized Hunter–Saxton system in the periodic setting. We first prove a persistence result for the solutions. Then for some particular choices of the parameters (α, κ), we show the precise blow-up scenarios and the existence of global solutions to the generalized Hunter–Saxton system under proper assumptions on the initial data. This significantly improves recent results.