论文标题
Lipschitz的弗拉索夫 - 马克斯韦尔系统的连续解决方案具有导体边界条件
Lipschitz continuous solutions of the Vlasov-Maxwell systems with a conductor boundary condition
论文作者
论文摘要
我们认为相对论的血浆颗粒在$ 3 $ d的半空间中受到外部重力，其边界是完美的导体。当平均自由路径比电磁场的变化大得多时，碰撞效应可以忽略不计。作为有效的PDE，我们研究了相对论的Vlasov-Maxwell系统及其在当地时空的Lipschitz空间中的本地独特可溶性，对于几种基本的中镜（动力学）边界条件：流入，分散，分散和镜面反射边界条件。我们针对这些初始有限的价值问题构建弱解决方案，并根据解决方案本身的重量功能来研究其本地Lipschitz的连续性。最后，我们通过使用规律性估计并意识到Lipschitz连续空间的边界的高斯定律证明了解决方案的独特性。
We consider relativistic plasma particles subjected to an external gravitation force in a $3$D half space whose boundary is a perfect conductor. When the mean free path is much bigger than the variation of electromagnetic fields, the collision effect is negligible. As an effective PDE, we study the relativistic Vlasov-Maxwell system and its local-in-time unique solvability in the space-time locally Lipschitz space, for several basic mesoscopic (kinetic) boundary conditions: the inflow, diffuse, and specular reflection boundary conditions. We construct weak solutions to these initial-boundary value problems and study their locally Lipschitz continuity with the aid of a weight function depending on the solutions themselves. Finally, we prove the uniqueness of a solution, by using regularity estimate and realizing the Gauss's law at the boundary within Lipschitz continuous space.
