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On the transport operators arising from linearizing the Vlasov-Poisson or Einstein-Vlasov system about isotropic steady states

Title data

Rein, Gerhard ; Straub, Christopher:
On the transport operators arising from linearizing the Vlasov-Poisson or Einstein-Vlasov system about isotropic steady states.
In: Kinetic and Related Models. Vol. 13 (October 2020) Issue 5 . - pp. 933-949.
ISSN 1937-5077
DOI: https://doi.org/10.3934/krm.2020032

Abstract in another language

If the Vlasov-Poisson or Einstein-Vlasov system is linearized about an isotropic steady state, a linear operator arises the properties of which are relevant in the linear as well as nonlinear stability analysis of the given steady state.
We prove that when defined on a suitable Hilbert space and equipped with the proper domain of definition this transport operator $\T$ is skew-adjoint, i.e.,
$\T^\ast = - \T$.
In the Vlasov-Poisson case we also determine the kernel of this operator.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Vlasov-Poisson system; Einstein-Vlasov system; linearization;
skew-adjointness; transport operator
Subject classification: Primary: 85A05, 47F05; Secondary: 35B35, 35Q75
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics > Professor Applied Mathematics - Univ.-Prof. Dr. Gerhard Rein
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 11 Sep 2020 07:02
Last Modified: 11 Sep 2020 07:02
URI: https://eref.uni-bayreuth.de/id/eprint/56877