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

Griffin-Pickering, Megan and Iacobelli, Mikaela (2021) 'Global well-posedness for the Vlasov-Poisson system with massless electrons in the 3-dimensional torus.', Communications in partial differential equations., 46 (10). pp. 1892-1939.


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.

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Publisher statement: 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 (, 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.
Date accepted:28 March 2021
Date deposited:20 May 2021
Date of first online publication:11 May 2021
Date first made open access:20 May 2021

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