Diophantine Conditions in Well-Posedness Theory of Coupled KdV-Type Systems: Local Theory
| dc.creator | Oh, Tadahiro | |
| dc.date | 2009-04-18 | |
| dc.date.accessioned | 2026-07-07T13:05:46Z | |
| dc.date.available | 2026-07-07T13:05:46Z | |
| dc.description | We consider the local well-posedness problem of a one-parameter family of coupled KdV-type systems both in the periodic and non-periodic setting. In particular, we show that certain resonances occur, closely depending on the value of a coupling parameter αwhen α\ne 1. In the periodic setting, we use the Diophantine conditions to characterize the resonances, and establish sharp local well-posedness of the system in H^s(\mathbb{T}_λ), s \geq s^\ast, where s^\ast = s^\ast(α) \in ({1/2}, 1] is determined by the Diophantine characterization of certain constants derived from the coupling parameter α. We also present a sharp local (and global) result in L^2(\mathbb{R}). In the appendix, we briefly discuss the local well-posedness result in H^{-{1/2}}(\mathbb{T}_λ) for α= 1 without the mean 0 assumption, by introducing the vector-valued X^{s, b} spaces. | |
| dc.description | 31 pages. To appear in Internat. Math. Res. Not. "Global Theory" is available in Electron. J. Diff. Eqns | |
| dc.identifier | https://arxiv.org/abs/0904.2813 | |
| dc.identifier | http://arxiv.org/abs/0904.2813 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/227598 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q53 | |
| dc.title | Diophantine Conditions in Well-Posedness Theory of Coupled KdV-Type Systems: Local Theory | |
| dc.type | text |