论文标题
希尔伯特（Hilbert）扩展库仑碰撞动力学模型
Hilbert Expansion for Coulomb Collisional Kinetic Models
论文作者
论文摘要
相对论弗拉索夫 - 马克斯韦 - 兰道（R-VML）系统和相对论兰道方程（R-LAN）是描述电子气体动力学的基本模型。在本文中，我们引入了一种新型的加权能力方法，并确定了希尔伯特（Hilbert）扩展对R-VML系统和R-LAN方程的有效性。随着Knudsen数量缩小到零，我们严格地证明了相对论的Euler-Maxwell极限和相对论Euler的极限。这成功解决了关于Landau型方程的流体动力限制的长期开放问题。
The relativistic Vlasov-Maxwell-Landau (r-VML) system and the relativistic Landau equation (r-LAN) are fundamental models that describe the dynamics of an electron gas. In this paper, we introduce a novel weighted energy method and establish the validity of the Hilbert expansion for the r-VML system and r-LAN equation. As the Knudsen number shrinks to zero, we rigorously demonstrate the relativistic Euler-Maxwell limit and relativistic Euler limit, respectively. This successfully resolves the long-standing open problem regarding the hydrodynamic limits of Landau-type equations.
