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Global existence for the generalized two-component Hunter-Saxton system. (English) Zbl 1255.35188
Summary: 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 \((\alpha,\kappa)\), 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.

MSC:
35Q51 Soliton equations
35B44 Blow-up in context of PDEs
35Q35 PDEs in connection with fluid mechanics
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