Global well-posedness of Vlasov–Poisson-type systems in bounded domains

Cesbron, Ludovic; Iacobelli, Mikaela

doi:10.2140/apde.2023.16.2465

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Global well-posedness of Vlasov–Poisson-type systems in bounded domains

Ludovic Cesbron and Mikaela Iacobelli

Vol. 16 (2023), No. 10, 2465–2494

DOI: 10.2140/apde.2023.16.2465

Abstract

In this paper we prove global existence of classical solutions to the Vlasov–Poisson and ionic Vlasov–Poisson models in bounded domains. On the boundary, we consider the specular reflection boundary condition for the Vlasov equation and either homogeneous Dirichlet or Neumann conditions for the Poisson equations.

Keywords

Vlasov–Poisson, well-posedness, massless electrons, bounded domains

Mathematical Subject Classification

Primary: 35Q82, 35Q83, 76N10, 82C70

Milestones

Received: 30 August 2021

Accepted: 22 March 2022

Published: 11 December 2023

Authors

Ludovic Cesbron
Department of Mathematics ETH Zürich Zurich Switzerland	Laboratoire AGM CY Cergy Paris Université France

Mikaela Iacobelli
Department of Mathematics ETH Zürich Zurich Switzerland

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Vol. 16, No. 10, 2023