Regular Lagrangian flow for wavelike vector fields and the Vlasov-Maxwell system

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2024-10-01 DOI:10.1016/j.jde.2024.09.051

Henrique Borrin

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引用次数: 0

Abstract

In this paper, we study the Lagrangian structure of Vlasov-Maxwell system, that is, by using a suitable notion of flow, we prove that if the densities

ρ, j

are integrable in spacetime, and the charge acceleration

\partial_{t} j

and

\partial_{t t} j

(or

\nabla \partial_{t} j

) are integrable functions in spacetime, then renormalized and distributional solutions of the system are the transport of the initial condition by its flow. We study more general vector fields, with wavelike structure in the sense that it has finite speed of propagation, generalizing the vector fields studied in [6]. The result is a extension of those obtained by Ambrosio, Colombo, and Figalli [2] for the Vlasov-Poisson system, and by the author and Marcon [5] for relativistic Vlasov-systems with quasistatic approximations of Maxwell's equations.

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波状矢量场的正则拉格朗日流和弗拉索夫-麦克斯韦系统

在本文中，我们研究了 Vlasov-Maxwell 系统的拉格朗日结构，即通过使用合适的流概念，证明如果密度 ρ,j 在时空中是可积分的，电荷加速度 ∂tj 和 ∂ttj （或 ∇∂tj）在时空中是可积分的函数，那么系统的重正化和分布解就是其流对初始条件的传输。我们研究的是更一般的矢量场，在传播速度有限的意义上具有波状结构，是对 [6] 中研究的矢量场的推广。这一结果是 Ambrosio、Colombo 和 Figalli [2] 对 Vlasov-Poisson 系统，以及作者和 Marcon [5] 对麦克斯韦方程准静态近似的相对论 Vlasov 系统所获得结果的扩展。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics