Details

Autor(en) / Beteiligte

• Neiss, Robert Axel

Titel

Generalized Symplectization of Vlasov Dynamics and Application to the Vlasov–Poisson System

Ist Teil von

• Archive for rational mechanics and analysis, 2019-01, Vol.231 (1), p.115-151

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2019

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this paper, we study a Hamiltonian structure of the Vlasov–Poisson system, first mentioned by Fröhlich et al. (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 L 2 integrable functions α on the one particle phase space R Z 2 d ; s.t. f = α 2 is a solution of a collisionless Boltzmann equation. The only requirement is a sufficiently regular energy functional on a subspace of distribution functions f ∈ L 1 . Secondly, we give a full well-posedness theory for the obtained system corresponding to Vlasov–Poisson in d ≧ 3 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.