论文标题
可压缩的Euler-Maxwell限制全球平滑解决方案对Vlasov-Maxwell-Boltzmann系统
Compressible Euler-Maxwell limit for global smooth solutions to the Vlasov-Maxwell-Boltzmann system
论文作者
论文摘要
Vlasov-Maxwell-Boltzmann系统和可压缩的Euler-Maxwell系统给出了等离子体物理学中的两个基本模型，这些模型分别捕获了分别在动力学和流体水平的自一致的电磁相互作用下等离子体的复杂动力学。由于Knudsen Number $ \ Varepsilon $倾向于零，因此严格地证明从前者到后者的流体动力限制的正当限制是一个长期的开放问题。在本文中，如果仅考虑电子动力学，在整个空间中，在整个空间中，对两个系统的平滑解决方案的问题给出了肯定的答案。还可以为精心准备的数据获得$ \ varepsilon $中$ \ varepsilon $的明确收敛速率。为了证明，由于经典运输运营商对当地的麦克斯韦人的作用，大速度的立方生长发生了一个主要困难，我们开发了新的$ \ varepsilon $依赖性能量估计，基于宏观微分解以在可压缩设置中表征差异极限。
Two fundamental models in plasma physics are given by the Vlasov-Maxwell-Boltzmann system and the compressible Euler-Maxwell system which both capture the complex dynamics of plasmas under the self-consistent electromagnetic interactions at the kinetic and fluid levels, respectively. It has remained a long-standing open problem to rigorously justify the hydrodynamic limit from the former to the latter as the Knudsen number $\varepsilon$ tends to zero. In this paper we give an affirmative answer to the problem for smooth solutions to both systems near constant equilibrium in the whole space in case when only the dynamics of electrons is taken into account. The explicit rate of convergence in $\varepsilon$ over an almost global time interval is also obtained for well-prepared data. For the proof, one of main difficulties occurs to the cubic growth of large velocities due to the action of the classical transport operator on local Maxwellians and we develop new $\varepsilon$-dependent energy estimates basing on the macro-micro decomposition to characterize the asymptotic limit in the compressible setting.
