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

  • * Corresponding author: Gerhard Rein

    * Corresponding author: Gerhard Rein 
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  • 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 $ {\mathcal T} $ is skew-adjoint, i.e., $ {\mathcal T}^\ast = - {\mathcal T} $. In the Vlasov-Poisson case we also determine the kernel of this operator.

    Mathematics Subject Classification: Primary: 85A05, 47F05; Secondary: 35B35, 35Q75.


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