论文标题
非切割vlasov-Poisson-Boltzmann系统的稀有波的稳定性具有物理边界
Stability of Rarefaction Waves for the Non-cutoff Vlasov-Poisson-Boltzmann System with Physical Boundary
论文作者
论文摘要
在本文中，我们关注三维空间空间中的弗拉索夫 - 波森 - 波尔茨曼（VPB）系统，而在具有或没有物理边界条件的矩形管中，没有角截止。在一维压缩欧拉方程的稀疏波解决方案给出的宏观量的局部麦克斯威尔式附近，我们建立了具有周期性或镜面反射边界条件的cauchy问题的平面稀有波解决方案的时间 - 异常稳定性。特别是，我们成功地将物理边界（即镜面反射边界）引入了描述动力学方程波模式的模型。此外，我们将非切割碰撞内核而不是截止核心对待。作为一个简化的模型，我们还考虑了Boltzmann方程的稀有波解决方案的稳定性和大时间行为。
In this paper, we are concerned with the Vlasov-Poisson-Boltzmann (VPB) system in three-dimensional spatial space without angular cutoff in a rectangular duct with or without physical boundary conditions. Near a local Maxwellian with macroscopic quantities given by rarefaction wave solution of one-dimensional compressible Euler equations, we establish the time-asymptotic stability of planar rarefaction wave solutions for the Cauchy problem to VPB system with periodic or specular-reflection boundary condition. In particular, we successfully introduce physical boundaries, namely, specular-reflection boundary, to the models describing wave patterns of kinetic equations. Moreover, we treat the non-cutoff collision kernel instead of the cutoff one. As a simplified model, we also consider the stability and large time behavior of the rarefaction wave solution for the Boltzmann equation.
