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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
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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