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The Einstein-Vlasov system in maximal areal coordinates : Local existence and continuation

Title data

Günther, Sebastian ; Rein, Gerhard:
The Einstein-Vlasov system in maximal areal coordinates : Local existence and continuation.
In: Kinetic & Related Models. Vol. 15 (2022) Issue 4 . - pp. 681-719.
ISSN 1937-5077
DOI: https://doi.org/10.3934/krm.2021040

Abstract in another language

We consider the spherically symmetric, asymptotically flat Einstein-Vlasov system in maximal areal coordinates. The latter coordinates have been used both in analytical and numerical investigations of the Einstein-Vlasov system, but neither a local existence theorem nor a suitable continuation criterion has so far been established for the corresponding nonlinear system of PDEs. We close this gap. Although the analysis follows lines similar to the corresponding result in Schwarzschild coordinates, essential new difficulties arise from to the much more complicated form which the field equations take, while at the same time it becomes easier to control the necessary, highest order derivatives of the solution. The latter observation may be useful in subsequent investigations.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Einstein-Vlasov system; maximal areal coordinates; local existence;
continuation of solutions
Subject classification: Primary: 35Q85, 35Q76; Secondary: 85A05
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
Profile Fields > Advanced Fields > Nonlinear Dynamics
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
Profile Fields
Profile Fields > Advanced Fields
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 04 Feb 2022 07:52
Last Modified: 24 Jun 2022 10:10
URI: https://eref.uni-bayreuth.de/id/eprint/68581