Existence and non-uniqueness of stationary states for the Vlasov–Poisson equation on R3 subject to attractive background charges

We prove the existence of stationary solutions for the density of an infinitely extended plasma interacting with an arbitrary configuration of background charges. Furthermore, we show that the solution cannot be unique if the total charge of the background is attractive. In this case, infinitely man...

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Bibliographic Details
Published inSN partial differential equations and applications Vol. 4; no. 4; p. 30
Main Author Winter, Raphael
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.08.2023
Subjects
Analysis
Kinetic Theory
Mathematical and Computational Biology
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Original Paper
Partial Differential Equations
Theoretical
35Q83
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Summary:We prove the existence of stationary solutions for the density of an infinitely extended plasma interacting with an arbitrary configuration of background charges. Furthermore, we show that the solution cannot be unique if the total charge of the background is attractive. In this case, infinitely many different stationary solutions exist. The non-uniqueness can be explained by the presence of trapped particles orbiting the attractive background charge.
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ISSN:2662-2963
2662-2971
2662-2971
DOI:10.1007/s42985-023-00241-3