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Sharp Asymptotics for the Solutions of the Three-Dimensional Massless Vlasov–Maxwell System with Small Data
Annales Henri Poincaré ( IF 1.5 ) Pub Date : 2020-11-20 , DOI: 10.1007/s00023-020-00978-2
Léo Bigorgne

This paper is concerned with the asymptotic properties of the small data solutions to the massless Vlasov–Maxwell system in 3d. We use vector field methods to derive almost optimal decay estimates in null directions for the electromagnetic field, the particle density and their derivatives. No compact support assumption in x or v is required on the initial data, and the decay in v is in particular initially optimal. Consistently with Proposition 8.1 of Bigorgne (Asymptotic properties of small data solutions of the Vlasov–Maxwell system in high dimensions. arXiv:1712.09698, 2017), the Vlasov field is supposed to vanish initially for small velocities. In order to deal with the slow decay rate of the solutions near the light cone and to prove that the velocity support of the particle density remains bounded away from 0, we make crucial use of the null properties of the system.



中文翻译:

带有小数据的三维无质量Vlasov-Maxwell系统解的尖锐渐近

本文关注无质量Vlasov-Maxwell系统在3 d内的小数据解的渐近性质。我们使用矢量场方法在电磁场,粒子密度及其导数的零方向上得出几乎最佳的衰减估计。初始数据不需要xv的紧凑支持假设,并且v的衰减最初是最佳的。与Bigorgne命题8.1(高维Vlasov-Maxwell系统的小数据解的渐近性质。arXiv:1712.09698,2017)一致,Vlasov场最初在小速度时消失。为了处理光锥附近溶液的缓慢衰减速率并证明粒子密度的速度支持保持远离0有界,我们至关重要地利用了系统的零性质。

更新日期:2020-11-21
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