# Global existence for the generalized two-component Hunter-Saxton system - Mathematics > Analysis of PDEs

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Abstract: We study the global existence of solutions to a two-component generalizedHunter-Saxton system in the periodic setting. We first prove a persistenceresult of the solutions. Then for some particular choices of parameters$\alpha, \kappa$, we show the precise blow-up scenarios and the existence ofglobal solutions to the generalized Hunter-Saxton system under properassumptions on the initial data. This significantly improves recent resultsobtained in M. Wunsch, DCDS Ser. B 12 2009, 647-656 and M. Wunsch, SIAM J.Math. Anal. 42 2010, 1286-1304.

Autor: Hao Wu, Marcus Wunsch

Fuente: https://arxiv.org/