## 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 Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics |

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 |