Global Hilbert Expansion for the Relativistic Vlasov–Maxwell–Boltzmann System
Global Hilbert Expansion for the Relativistic Vlasov–Maxwell–Boltzmann System
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DOI：
10.1007/s00220-021-04079-x
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发表时间：
2020-01
影响因子：
2.4
通讯作者：
Yan Guo;Qinghua Xiao
中科院分区：
文献类型：
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作者：
Yan Guo;Qinghua Xiao
考虑相对论Vlasov-Maxwell-Boltzmann系统，该系统描述了在固定离子背景下电子气的动力学。由于最近的作品Germain和Masmudi(Ann Sciéc Norm Supér 47(3)：469-503,2014)，郭等人。(《数学物理学报》55(12)：123102,2014年)和邓等人。(ARCH Ratio Mech Anal225(2)：771-871,2017)，我们建立了其Hilbert展开式的全局时间有效性，并导出了当平均自由程趋于零时的极限相对论Euler-Maxwell系统。我们的方法是基于电磁场的框架和Glassey-Strauss表示，辅以估计和估计来控制特征曲线和相应的范数。
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 Germain and Masmoudi (Ann Sci Éc Norm Supér 47(3):469–503, 2014), Guo et al. (J Math Phys 55(12):123102, 2014) and Deng et al. (Arch Ration Mech Anal 225(2):771–871, 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 theframework and the Glassey–Strauss Representation of the electromagnetic field, with auxiliaryestimates andestimates to control the characteristic curves and correspondingnorm.