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

Griffin-Pickering, Megan; Iacobelli, Mikaela

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
• Public URL: https://durham-repository.worktribe.com/output/1274846