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We construct (modified) scattering operators for the Vlasov-Poisson system in three dimensions, mapping small asymptotic dynamics as $t\to -\infty$ to asymptotic dynamics as $t\to +\infty$. The main novelty is the construction of modified…

Analysis of PDEs · Mathematics 2021-01-06 Patrick Flynn , Zhimeng Ouyang , Benoit Pausader , Klaus Widmayer

The purpose of this paper is twofold. In the first part, we provide a new proof of the global existence of the solutions to the Vlasov-Maxwell system with a small initial distribution function. Our approach relies on vector field methods,…

Analysis of PDEs · Mathematics 2025-03-05 Léo Bigorgne

We prove that for any global solution to the Vlasov-Maxwell system arising from compactly supported data, and such that the electromagnetic field decays fast enough, the distribution function exhibits a modified scattering dynamic. In…

Analysis of PDEs · Mathematics 2025-06-23 Emile Breton

We study the theory of scattering for the Maxwell-Schr"odinger system in space dimension 3,in the Coulomb gauge.In the special case of vanishing asymptotic magnetic field,we prove the existence of modified wave operators for that system…

Analysis of PDEs · Mathematics 2015-06-26 J. Ginibre , G. Velo

We consider the relativistic Vlasov-Maxwell system in three dimensions and study the limiting asymptotic behavior as $t \to \infty$ of solutions launched by small, compactly supported initial data. In particular, we prove that such…

Analysis of PDEs · Mathematics 2024-03-12 Stephen Pankavich , Jonathan Ben-Artzi

We study the long-time asymptotic behavior of small-data solutions to the three-dimensional Vlasov--Riesz system with the inverse power-law potential $\lambda |x|^{-\alpha}$ in the strictly long-range regime ($0 < \alpha < 1$). By…

Analysis of PDEs · Mathematics 2026-04-07 Younghun Hong , Stephen Pankavich

We study the theory of scattering for the Maxwell-Schr"odinger system in space dimension 3, in the Coulomb gauge. We prove the existence of modified wave operators for that system with no size restriction on the Schr"odinger and Maxwell…

Analysis of PDEs · Mathematics 2015-06-26 J. Ginibre , G. Velo

We continue the study of scattering theory for the system consisting of a Schr"odinger equation and a wave equation with a Yukawa type coupling in space dimension 3. In a previous paper we proved the existence of modified wave operators for…

Analysis of PDEs · Mathematics 2007-05-23 J. Ginibre , G. Velo

We prove small data modified scattering for the Vlasov-Poisson system in dimension $d=3$ using a method inspired from dispersive analysis. In particular, we identify a simple asymptotic dynamic related to the scattering mass.

Analysis of PDEs · Mathematics 2020-05-08 Alexandru D. Ionescu , Benoit Pausader , Xuecheng Wang , Klaus Widmayer

We review the proof of existence and uniqueness of solutions of the Maxwell-Schr"odinger system in a neighborhood of infinity in time, with prescribed asymptotic behaviour defined in terms of asymptotic data, without any restriction on the…

Analysis of PDEs · Mathematics 2008-04-04 J. Ginibre , G. Velo

We study the relativistic and non-relativistic Vlasov equation driven by short-range interaction potentials and identify the large time dynamics of solutions. In particular, we construct global-in-time solutions launched from small initial…

Analysis of PDEs · Mathematics 2025-09-11 Younghun Hong , Stephen Pankavich

We consider the Vlasov--Poisson system with a repulsive harmonic potential and prove the (modified) scattering of solutions, as well as the existence of wave operators, in any spatial dimension $d\geq 2$. The main novelty of this work is…

Analysis of PDEs · Mathematics 2026-02-26 Wenrui Huang , Hyunwoo Kwon

We consider an asymptotic behavior of solutions to the Vlasov-Riesz system of order $\alpha$ in $\mathbb{R}^3$ which is a kinetic model induced by Riesz interactions. We prove small data scattering when $1/2<\alpha<1$ and modified…

Analysis of PDEs · Mathematics 2025-09-30 Wenrui Huang , Hyunwoo Kwon

We study the theory of scattering for the Maxwell-Schr"odinger system in the Coulomb gauge in space dimension 3. We prove in particular the existence of modified wave operators for that system with no size restriction on the magnetic field…

Analysis of PDEs · Mathematics 2007-05-23 J. Ginibre , G. Velo

In this paper, we study small data solutions to the Vlasov-Poisson system with the simplest external potential, for which unstable trapping holds for the associated Hamiltonian flow. First, we provide a new proof of global existence for…

Analysis of PDEs · Mathematics 2023-10-30 Léo Bigorgne , Anibal Velozo Ruiz , Renato Velozo Ruiz

We construct global-in-time classical solutions to the nonlinear Vlasov-Maxwell system in a three-dimensional half-space beyond the vacuum scattering regime. Our approach combines the construction of stationary solutions to the associated…

Analysis of PDEs · Mathematics 2025-10-07 Jin Woo Jang , Chanwoo Kim

This paper is concerned with the analysis of time-harmonic electromagnetic scattering from plasmonic inclusions in the finite frequency regime beyond the quasi-static approximation. The electric permittivity and magnetic permeability in the…

Analysis of PDEs · Mathematics 2019-01-29 Hongjie Li , Shanqiang Li , Hongyu Liu , Xianchao Wang

We prove small data energy estimates of all orders of differentiability between past null infinity and future null infinity of de Sitter space for the conformally invariant Maxwell-scalar field system. This allows us to construct bounded…

Analysis of PDEs · Mathematics 2025-07-17 Grigalius Taujanskas

We continue the study of scattering theory for the system consisting of a Schr"odinger equation and a wave equation with a Yukawa type coupling in space dimension 3. In previous papers, we proved the existence of modified wave operators for…

Analysis of PDEs · Mathematics 2007-05-23 J. Ginibre , G. Velo

We consider the repulsive Vlasov-Poisson system in dimension $d \geq 4$. A sufficient condition on the decay rate of the associated electric field is presented that guarantees the scattering and determination of the complete asymptotic…

Analysis of PDEs · Mathematics 2023-06-08 Stephen Pankavich
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