论文标题
相对论弗拉索夫 - 马克斯韦 - 博尔兹曼系统的全球希尔伯特扩展
Global Hilbert expansion for the relativistic Vlasov-Maxwell-Boltzmann system
论文作者
论文摘要
考虑相对论的Vlasov-Maxwell-Boltzmann系统在存在固定离子背景的情况下描述电子气体的动力学。 Thanks to recent works \cite{Germain-Masmoudi-ASENS-2014, Guo-Ionescu-Pausader-JMP-2014} and \cite{Deng-Ionescu-Pausader-ARMA-2017}, we establish the global-in-time validity of its Hilbert expansion and derive the limiting relativistic Euler-Maxwell system as the mean free path goes to zero.我们的方法基于$ l^2-l^{\ infty} $框架和电磁场的Glassey-Strauss表示，具有辅助$ H^1 $估计和$ W^{1，\ infty} $估计，以控制特征性曲线和相应的$ l^{\ f^{\ infty} $ norm。
Consider the relativistic Vlasov-Maxwell-Boltzmann system describing the dynamics of an electron gas in the presence of a fixed ion background. Thanks to recent works \cite{Germain-Masmoudi-ASENS-2014, Guo-Ionescu-Pausader-JMP-2014} and \cite{Deng-Ionescu-Pausader-ARMA-2017}, we establish the global-in-time validity of its Hilbert expansion and derive the limiting relativistic Euler-Maxwell system as the mean free path goes to zero. Our method is based on the $L^2-L^{\infty}$ framework and the Glassey-Strauss Representation of the electromagnetic field, with auxiliary $H^1$ estimate and $W^{1,\infty}$ estimates to control the characteristic curves and corresponding $L^{\infty}$ norm.
