Global Existence for the Generalized Two-Component Hunter–Saxton System
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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.
Mathematics Subject Classification (2010)Primary 35B10 Secondary 35Q35
KeywordsGeneralized Hunter–Saxton system Global existence Blow-up scenario
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