Quasi-periodic dynamics of desingularized vortex models
dc.contributor.author | Lim, Chjan C. | en_US |
dc.date.accessioned | 2006-04-07T20:46:30Z | |
dc.date.available | 2006-04-07T20:46:30Z | |
dc.date.issued | 1989-07 | en_US |
dc.identifier.citation | Lim, Chjan C. (1989/07)."Quasi-periodic dynamics of desingularized vortex models." Physica D: Nonlinear Phenomena 37(1-3): 497-507. <http://hdl.handle.net/2027.42/27871> | en_US |
dc.identifier.uri | http://www.sciencedirect.com/science/article/B6TVK-46TYX7P-21/2/9ecffbc5d408af18b28dfd7cf0d23993 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/27871 | |
dc.description.abstract | Sufficient conditions for the existence of quasi-periodic solutions of two different desingularized vortex models for 2-dimensional Euler flows are derived. One of these models is the vortex blob model for the evolution of a periodic vortex sheet and the other is a second order elliptic moment model (DEMM) for the evolution of widely separated vortex regions. The method involves the identification of the well-known point vortex Hamiltonian term in both models. A transformation to new canonical variables (the JL-coordinates) and the definition of special open sets in phase space (the cone sets) puts the Hamiltonians considered into nearly integrable form. KAM-theory is used to prove the desired results for arbitrary degrees of freedom and almost arbitrary circulations in these models. A rigorous validification of the DEMM assumption is obtained. In view of the lack of a rigorous theory for vortex sheet roll-up past the critical time, the dynamical system approach presented here provides an alternative method for studying the macroscopic structures formed in the post-critical period. | en_US |
dc.format.extent | 1128205 bytes | |
dc.format.extent | 3118 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Elsevier | en_US |
dc.title | Quasi-periodic dynamics of desingularized vortex models | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/27871/1/0000285.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1016/0167-2789(89)90154-1 | en_US |
dc.identifier.source | Physica D: Nonlinear Phenomena | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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