Neiss, Robert Axel (2019). Generalized Symplectization of Vlasov Dynamics and Application to the Vlasov-Poisson System. Arch. Ration. Mech. Anal., 231 (1). S. 115 - 152. NEW YORK: SPRINGER. ISSN 1432-0673
Full text not available from this repository.Abstract
In this paper, we study a Hamiltonian structure of the Vlasov-Poisson system, first mentioned by Frohlich etal. (Commun Math Phys 288:1023-1058, 2009). To begin with, we give a formal guideline to derive a Hamiltonian on a subspace of complex-valued L2 integrable functions on the one particle phase space RZ2d; s.t. f=2 is a solution of a collisionless Boltzmann equation. The only requirement is a sufficiently regular energy functional on a subspace of distribution functions fL1. Secondly, we give a full well-posedness theory for the obtained system corresponding to Vlasov-Poisson in d3 dimensions. Finally, we adapt the classical globality results (Lions and Perthame in Invent Math 105:415-430, 1991; Pfaffelmoser in J Differ Equ 95:281-303, 1992; Schaeffer in Commun Partial Differ Equ 16(8-9):1313-1335, 1991) for d =3 to the generalized system.
| Item Type: | Journal Article | ||||||||
| Creators: |
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| URN: | urn:nbn:de:hbz:38-140045 | ||||||||
| DOI: | 10.1007/s00205-018-1275-8 | ||||||||
| Journal or Publication Title: | Arch. Ration. Mech. Anal. | ||||||||
| Volume: | 231 | ||||||||
| Number: | 1 | ||||||||
| Page Range: | S. 115 - 152 | ||||||||
| Date: | 2019 | ||||||||
| Publisher: | SPRINGER | ||||||||
| Place of Publication: | NEW YORK | ||||||||
| ISSN: | 1432-0673 | ||||||||
| Language: | English | ||||||||
| Faculty: | Unspecified | ||||||||
| Divisions: | Unspecified | ||||||||
| Subjects: | no entry | ||||||||
| Uncontrolled Keywords: |
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| Refereed: | Yes | ||||||||
| URI: | http://kups.ub.uni-koeln.de/id/eprint/14004 |
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