论文标题
具有镜面边界条件的Vlasov-Poisson-Landau系统
The Vlasov-Poisson-Landau System with the Specular-Reflection Boundary Condition
论文作者
论文摘要
我们考虑Vlasov-Poisson-Landau系统，这是一种经典的模型，用于通过库仑碰撞及其自洽的静电场相互作用稀释的碰撞等离子体。我们在麦克斯韦平衡状态附近建立了全球稳定性和良好的度，并且在任何一般有限的域（包括托克马克设备中的圆环），在存在侧面反射边界条件下，在任何一般有限的域（包括圆环）中，对小初始扰动的一些规律性结果。我们提供了一个新的改进的$ l^{2} \ rightarrow l^{\ infty} $框架：$ l^{2} $ energy估算仅与$ s^{p} $估算的超顺抗方程相结合。
We consider the Vlasov-Poisson-Landau system, a classical model for a dilute collisional plasma interacting through Coulombic collisions and with its self-consistent electrostatic field. We establish global stability and well-posedness near the Maxwellian equilibrium state with decay in time and some regularity results for small initial perturbations, in any general bounded domain (including a torus as in a tokamak device), in the presence of specular reflection boundary condition. We provide a new improved $L^{2}\rightarrow L^{\infty }$ framework: $L^{2}$ energy estimate combines only with $S^{p}$ estimate for the ultra-parabolic equation.
