A Note on a Generalized Two Component Camassa-Holm System in Sobolev Spaces
| Autor: | Thompson, Ryan C. |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we consider a generalized two component Camassa-Holm system. Based on local well-posedness results and lifespan estimates, we establish sharpness of continuity on the data-to-solution map by showing that it is not uniformly continuous from product Sobolev spaces $H^s \times H^{s}$ to $C([0,T]; H^s \times H^{s})$. The proof of nonuniform dependence is based upon approximate solutions. |
| Databáze: | arXiv |
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