For Sobolev exponent s > 5=2, it is shown that the data-to-solution map for the2-component Camassa-Holm system is continuous from Hs x Hsô€€€-1 into C([0; T];Hs x Hsô€€€-1) but not uniformly continuous. The proof of non-uniform dependence on the initial data is based on the method of approximate solutions, delicate commutator and multiplier estimates, and well-posedness results for the solution and its lifespan. Also, the solution map is Holder continuous if the Hs x Hs-ô€€€1 norm is replaced by an Hr x Hrô€€€-1 norm for 0 r < s.
The Cauchy Problem for the CH2 System
Doctoral Dissertation
Abstract
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Author | Ryan Cole Thompson |
Advisor | Alex Himonas |
Contributor | Alex Himonas, Committee Chair |
Contributor | Gerard Misiolek, Committee Member |
Contributor | Yongtao Zhang, Committee Member |
Contributor | Alan Lindsay, Committee Member |
Degree Level | Doctoral Dissertation |
Degree Discipline | Mathematics |
Degree Name | PhD |
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Submission Date | 2015-03-16 |
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Record Visibility | Public |
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ThompsonRC032015D.pdf | 854 KB | application/pdf | Public |
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