Green’s Function and Pointwise Behavior of the One-Dimensional Vlasov–Maxwell–Boltzmann System
Green’s Function and Pointwise Behavior of the One-Dimensional Vlasov–Maxwell–Boltzmann System
复制标题
DOI：
10.1007/s00205-023-01906-4
复制
发表时间：
2023-08
影响因子：
2.5
通讯作者：
Hai-liang Li;Tong Yang;Mingying Zhong
中科院分区：
文献类型：
--
作者：
Hai-liang Li;Tong Yang;Mingying Zhong
研究了一维Vlasov-Maxwell-Boltzmann（VMB）系统绿色函数的点态时空行为。结果表明，绿色函数由速度在低频的宏观扩散波和惠更斯波，速度在高频的双曲波，奇异动力波和超前短波，以及在空间和时间上指数衰减的余项组成。请注意，这些高频双曲波是全新的，无法在玻尔兹曼方程和Vlasov-Poisson-Boltzmann系统中观察到。此外，我们建立了基于绿色函数的非线性VMB系统整体解的逐点时空估计。与Boltzmann方程和Vlasov-Poisson-Boltzmann系统相比，本文引入了一些新的思想，克服了粒子输运和电磁场旋转耦合效应带来的困难，研究了新的双曲波和奇异超前短波。
The pointwise space-time behavior of the Green’s function of the one-dimensional Vlasov–Maxwell–Boltzmann (VMB) system is studied in this paper. It is shown that the Green’s function consists of the macroscopic diffusive waves and Huygens waves with the speedat low-frequency, the hyperbolic waves with the speedat high-frequency, the singular kinetic and leading short waves, and the remaining term decaying exponentially in space and time. Note that these high-frequency hyperbolic waves are completely new and cannot be observed for the Boltzmann equation and the Vlasov–Poisson–Boltzmann system. In addition, we establish the pointwise space-time estimate of the global solution to the nonlinear VMB system based on the Green’s function. Compared to the Boltzmann equation and the Vlasov–Poisson–Boltzmann system, some new ideas are introduced to overcome the difficulties caused by the coupling effects of the transport of particles and the rotating of electro-magnetic fields, and investigate the new hyperbolic waves and singular leading short waves.