Regularity of weak solutions for the relativistic Vlasov–Maxwell system

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED Journal of Hyperbolic Differential Equations Pub Date : 2018-12-01 DOI:10.1142/S0219891618500212

N. Besse, Philippe Bechouche

引用次数: 8

Abstract

We investigate the regularity of weak solutions of the relativistic Vlasov–Maxwell system by using Fourier analysis and the smoothing effect of low velocity particles. This smoothing effect has been used by several authors (see Glassey and Strauss 1986; Klainerman and Staffilani, 2002) for proving existence and uniqueness of [Formula: see text]-regular solutions of the Vlasov–Maxwell system. This smoothing mechanism has also been used to study the regularity of solutions for a kinetic transport equation coupled with a wave equation (see Bouchut, Golse and Pallard 2004). Under the same assumptions as in the paper “Nonresonant smoothing for coupled wave[Formula: see text]+[Formula: see text]transport equations and the Vlasov–Maxwell system”, Rev. Mat. Iberoamericana 20 (2004) 865–892, by Bouchut, Golse and Pallard, we prove a slightly better regularity for the electromagnetic field than the one showed in the latter paper. Namely, we prove that the electromagnetic field belongs to [Formula: see text], with [Formula: see text].

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相对论性Vlasov–Maxwell系统弱解的正则性

利用傅里叶分析和低速粒子的平滑效应，研究了相对论性Vlasov-Maxwell系统弱解的规律性。这种平滑效应已经被一些作者使用过(见Glassey and Strauss 1986;Klainerman和Staffilani, 2002)证明了Vlasov-Maxwell系统的正则解的存在性和唯一性。这种平滑机制也被用于研究与波动方程耦合的动力学输运方程解的规律性(见Bouchut, Golse和Pallard 2004)。在与Bouchut, Golse和Pallard的论文“耦合波的非共振平滑[公式:见文]+[公式:见文]输运方程和Vlasov-Maxwell系统”，Rev. Mat. Iberoamericana 20(2004) 865-892相同的假设下，我们证明了一个比后一篇论文稍好的电磁场正则性。即证明电磁场属于[公式:见文]，用[公式:见文]。

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 Hyperbolic Differential Equations 数学-物理：数学物理

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in: Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions. Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc. Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations. Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc. General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations. Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.

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