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In this work, we study the quasineutral limit of the one-dimensional Vlasov-Poisson equation for ions with massless thermalized electrons. We prove new weak-strong stability estimates in the Wasserstein metric that allow us to extend and…

Analysis of PDEs · Mathematics 2014-12-15 Daniel Han-Kwan , Mikaela Iacobelli

In this paper, we establish the stability of the quasineutral limit for the ionic Vlasov-Poisson system under perturbations exponentially small in Wasserstein sense. Notably, we emphasize that exponential smallness is a necessary condition…

Analysis of PDEs · Mathematics 2024-03-08 Megan Griffin-Pickering , Mikaela Iacobelli

This article presents an overview of quasineutral limits in plasma models. Starting from the Vlasov-Poisson system, it explains the role of the Debye length, the emergence of a kinetic incompressibility constraint, and the stability issues…

Analysis of PDEs · Mathematics 2026-05-28 Mikaela Iacobelli

We study the quasineutral limit of a Vlasov-Poisson system that describes the dynamics of ions in a plasma. We handle data with Sobolev regularity under the sharp assumption that the profile of the initial data in the velocity variable…

Analysis of PDEs · Mathematics 2015-09-01 Daniel Han-Kwan , Frédéric Rousset

This work is concerned with the quasineutral limit of the Vlasov-Poisson system in two and three dimensions. We justify the formal limit for very small but rough perturbations of analytic initial data, generalizing the results of \cite{HI}…

Analysis of PDEs · Mathematics 2015-03-23 Daniel Han-Kwan , Mikaela Iacobelli

In this work, we propose a new numerical method for the Vlasov-Poisson system that is both asymptotically consistent and stable in the quasineutral regime, i.e. when the Debye length is small compared to the characteristic spatial scale of…

Numerical Analysis · Mathematics 2025-04-09 Alain Blaustein , Giacomo Dimarco , Francis Filbet , Marie-Hélène Vignal

Slow manifold reduction and the theory of Poisson-Dirac submanifolds are used to deduce a Hamiltonian formulation for a quasineutral limit of the planar, collisionless, magnetized Vlasov-Poisson system. Motion on the slow manifold models…

Mathematical Physics · Physics 2025-08-14 J. W. Burby , D. A. Kaltsas , P. J. Morrison , E. Tassi , G. N. Throumoulopoulos

We construct the approximate solutions to the Vlasov--Poisson system in a half-space, which arises in the study of the quasi-neutral limit problem in the presence of a sharp boundary layer, referred as to the plasma sheath in the context of…

Mathematical Physics · Physics 2024-01-17 Chang-Yeol Jung , Bongsuk Kwon , Masahiro Suzuki , Masahiro Takayama

Kinetic equations of Vlasov type are in widespread use as models in plasma physics. A well known example is the Vlasov-Poisson system for collisionless, unmagnetised plasma. In these notes, we discuss recent progress on the quasineutral…

Analysis of PDEs · Mathematics 2020-11-17 Megan Griffin-Pickering , Mikaela Iacobelli

We study the Vlasov-Poisson-Fokker-Planck system with uncertainty and multiple scales. Here the uncertainty, modeled by random variables, enters the solution through initial data, while the multiple scales lead the system to its high-field…

Analysis of PDEs · Mathematics 2017-10-18 Shi Jin , Yuhua Zhu

The Vlasov-Poisson system for ions is a kinetic equation for dilute, unmagnetised plasma. It describes the evolution of the ions in a plasma under the assumption that the electrons are thermalized. Consequently, the Poisson coupling for the…

Analysis of PDEs · Mathematics 2026-05-15 Megan Griffin-Pickering

In this paper, we study the Vlasov-Poisson system with massless electrons (VPME) near quasineutrality and with uncertainties. Based on the idea of reformulation on the Poisson equation by [P. Degond et.al., $\textit{Journal of Computational…

Numerical Analysis · Mathematics 2026-03-17 Guangwei Liu , Liu Liu , Yanli Wang

In this paper, we study the quasineutral limit (in other words the limit when the Debye length tends to zero) of Vlasov-Poisson like equations describing the behaviour of ions in a plasma. We consider massless electrons, with a charge…

Analysis of PDEs · Mathematics 2010-11-30 Daniel Han-Kwan

We investigate the stability of solutions to the Vlasov-Poisson system using the unifying framework of the kinetic Wasserstein distance, introduced by Iacobelli in (Section 4 in Arch. Ration. Mech. Anal. 244 (2022), no. 1, 27-50). This…

Analysis of PDEs · Mathematics 2025-03-26 Jonathan Junné , Alexandre Rege

This work is concerned with the quasineutral limit of the one-dimensional Vlasov-Poisson equation, for initial data close to stationary homogeneous profiles. Our objective is threefold: first, we provide a proof of the fact that the formal…

Analysis of PDEs · Mathematics 2015-06-18 Daniel Han-Kwan , Maxime Hauray

In light of recent work in the global well-posedness of solutions for an ionic Vlasov-Poisson system, as demonstrated by Griffin-Pickering and Iacobelli, the current work focuses on the moment propagation of the corresponding system in…

Analysis of PDEs · Mathematics 2026-01-13 Zhiwen Zhang

We study the finite Larmor radius regime for the Vlasov-Poisson system. The magnetic field is assumed to be uniform. We investigate this non linear problem in the two dimensional setting. We derive the limit model by appealing to…

Analysis of PDEs · Mathematics 2015-11-03 Mihaï Bostan , Aurélie Finot , Maxime Hauray

We study the quasineutral limit of the isothermal Euler-Poisson system describing a plasma made of ions and massless electrons. The analysis is achieved in a domain of $\R^3$ and thus extends former results by Cordier and Grenier [Comm.…

Analysis of PDEs · Mathematics 2011-12-02 David Gérard-Varet , Daniel Han-Kwan , Frédéric Rousset

We study the quasineutral limit for the relativistic Vlasov-Maxwell system in the framework of analytic regularity. Following the high regularity approach introduced by Grenier [44] for the Vlasov-Poisson system, we construct local-in-time…

Analysis of PDEs · Mathematics 2025-05-19 Antoine Gagnebin , Mikaela Iacobelli , Alexandre Rege , Stefano Rossi

We study smooth, spherically-symmetric solutions to the Vlasov-Poisson system and relativistic Vlasov-Poisson system in the plasma physical case. We construct solutions that initially possess arbitrarily small C^k norms for the charge…

Analysis of PDEs · Mathematics 2019-10-15 Katherine Zhiyuan Zhang
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