Global Existence for the Generalized Two-Component Hunter–Saxton System |
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| Authors: | Hao Wu Marcus Wunsch |
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| Institution: | 1. Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, 220 Han Dan Road, Shanghai, 200433, People’s Republic of China
2. Department of Mathematics, Swiss Federal Institute of Technology Zurich, Raemistrasse 101, 8092, Zurich, Switzerland
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| Abstract: | 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. |
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