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

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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
CreatorsEmailORCIDORCID Put Code
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:
EQUATIONSMultiple languages
Mathematics, Applied; MechanicsMultiple languages
Refereed: Yes


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