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Rein, Gerhard ; Straub, Christopher:
On the transport operators arising from linearizing the Vlasov-Poisson or Einstein-Vlasov system about isotropic steady states.
In: Kinetic & Related Models.
Bd. 13
(2020)
Heft 5
.
- S. 933-949.
ISSN 1937-5077
DOI: https://doi.org/10.3934/krm.2020032
Abstract
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∗=−T. In the Vlasov-Poisson case we also determine the kernel of this operator.