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Global well-posedness for the Vlasov-Poisson system with massless electrons in the 3-dimensional torus

Griffin-Pickering, Megan; Iacobelli, Mikaela

Global well-posedness for the Vlasov-Poisson system with massless electrons in the 3-dimensional torus Thumbnail


Authors

Megan Griffin-Pickering

Mikaela Iacobelli



Abstract

The Vlasov-Poisson system with massless electrons (VPME) is widely used in plasma physics to model the evolution of ions in a plasma. It differs from the Vlasov-Poisson system (VP) for electrons in that the Poisson coupling has an exponential nonlinearity that creates several mathematical difficulties. In particular, while global well-posedness in 3 D is well understood in the electron case, this problem remained completely open for the ion model with massless electrons. The aim of this paper is to fill this gap by proving uniqueness for VPME in the class of solutions with bounded density, and global existence of solutions with bounded density for a general class of initial data, generalising all the previous results known for VP.

Citation

Griffin-Pickering, M., & Iacobelli, M. (2021). Global well-posedness for the Vlasov-Poisson system with massless electrons in the 3-dimensional torus. Communications in Partial Differential Equations, 46(10), 1892-1939. https://doi.org/10.1080/03605302.2021.1913750

Journal Article Type Article
Acceptance Date Mar 28, 2021
Online Publication Date May 11, 2021
Publication Date 2021
Deposit Date May 20, 2021
Publicly Available Date May 20, 2021
Journal Communications in Partial Differential Equations
Print ISSN 0360-5302
Electronic ISSN 1532-4133
Publisher Taylor and Francis Group
Peer Reviewed Peer Reviewed
Volume 46
Issue 10
Pages 1892-1939
DOI https://doi.org/10.1080/03605302.2021.1913750

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Published Journal Article (Advance online version) (3.6 Mb)
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Publisher Licence URL
http://creativecommons.org/licenses/by-nc-nd/4.0/

Copyright Statement
Advance online version 2021 The Author(s). Published with license by Taylor and Francis Group, LLC
This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License
(http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium,
provided the original work is properly cited, and is not altered, transformed, or built upon in any way.




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