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 particular, our result applies to small data solutions constructed by Glassey and Strauss.
BigorgneL. (2020). Sharp asymptotic behavior of solutions of the 3D Vlasov–Maxwell system with small data. Communications in Mathematical Physics, 376(2), 893–992.
2.
BigorgneL. (2023b). Scattering map for the Vlasov–Maxwell system around source-free electromagnetic fields. arXiv: 2312.12214.
3.
BigorgneL. (2025). Global existence and modified scattering for the solutions to the Vlasov-Maxwell system with a small distribution function. Analysis & PDE, 18(3), 629–714.
4.
BigorgneL.RuizR. V. (2024). Late-time asymptotics of small data solutions for the Vlasov–Poisson system. arXiv: 2404.05812 [math.AP].
5.
BigorgneL.Velozo RuizA.Velozo RuizR. (2025). Modified scattering of small data solutions for the Vlasov–Poisson system with a repulsive potential. SIAM Journal on Mathematical Analysis, 57(1), 714–752.
6.
BretonE. (2025). A note on the non -asymptotic completeness of the Vlasov–Maxwell system. arXiv: 2509.04025.
7.
ChoiS. H.HaS. Y. (2011). Asymptotic behavior of the nonlinear vlasov equation with a self-consistent force. SIAM Journal on Mathematical Analysis, 43(5), 2050–2077.
8.
ChoiS. H.KwonS. (2016). Modified scattering for the Vlasov–Poisson system. Nonlinearity, 29(9), 2755.
9.
FlynnP.OuyangZ.PausaderB.WidmayerK. (2023). Scattering map for the Vlasov–Poisson system. Peking Mathematical Journal, 6(2), 365–392.
10.
GlasseyR. T.SchaefferJ. W. (1988). Global existence for the relativistic Vlasov–Maxwell system with nearly neutral initial data. Communications in Mathematical Physics, 119(3), 353–384.
11.
GlasseyR. T.StraussW. A. (1987). Absence of shocks in an initially dilute collisionless plasma. Communications in Mathematical Physics, 113(2), 191–208.
12.
IonescuA. D.PausaderB.WangX.WidmayerK. (2021). On the asymptotic behavior of solutions to the Vlasov–Poisson system. International Mathematics Research Notices, 2022(12), 8865–8889.
13.
LukJ.StrainR. M. (2016). Strichartz estimates and moment bounds for the relativistic Vlasov–Maxwell system. Archive for Rational Mechanics and Analysis, 219(1), 445–552.
14.
PankavichS. (2022). Asymptotic dynamics of dispersive, collisionless plasmas. Communications in Mathematical Physics, 391(2), 455–493.
15.
PankavichS.Ben-ArtziJ. (2024). Modified scattering of solutions to the relativistic Vlasov–Maxwell system inside the light cone. arXiv: 2306.11725 [math.AP].
16.
PausaderB.WidmayerK. (2021). Stability of a point charge for the Vlasov–Poisson system: The radial case. Communications in Mathematical Physics, 385(3), 1741–1769.
17.
PausaderB.WidmayerK.YangJ. (2024). Stability of a point charge for the repulsive Vlasov–Poisson system. Journal of the European Mathematical Society, Published online first.
18.
ReinG. (1990). Generic global solutions of the relativistic Vlasov–Maxwell system of plasma physics. Communications in Mathematical Physics, 135(1), 41–78.
19.
SchaefferJ. (2004). A small data theorem for collisionless plasma that includes high velocity particles. Indiana University Mathematics Journal, 53(1), 1–34.
20.
SchlueV.TaylorM. (2024). Inverse modified scattering and polyhomogeneous expansions for the Vlasov–Poisson system. arXiv: 2404.15885 [math.AP].
21.
WangX. (2022). Propagation of regularity and long time behavior of the 3D massive relativistic transport equation II: Vlasov–Maxwell system. Communications in Mathematical Physics, 389(2), 715–812.
22.
WeiD.YangS. (2021). On the 3D relativistic Vlasov–Maxwell system with large Maxwell field. Communications in Mathematical Physics, 383(3), 2275–2307.
