The Vlasov-Poisson-Landau system in a periodic box
The Vlasov-Poisson-Landau system in a periodic box
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DOI：
10.1090/s0894-0347-2011-00722-4
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发表时间：
2012-09
影响因子：
3.9
通讯作者：
Yan Guo
中科院分区：
文献类型：
--
作者：
Yan Guo
经典的弗拉索夫-泊松-朗道系统描述了碰撞等离子体与自身静电场相互作用的动力学以及它的掠射碰撞。这种掠食碰撞是由著名的Landau （Fokker-Planck）碰撞核模型，由Landau在1936年提出。对于初始数据具有较小的加权H范数，但具有较大的H（k3）范数且具有较高的速度矩，我们构造了该系统的全局唯一解。我们的构建是基于过去十年对朗道核的累积研究[G1] [SG1-3]，还有四个额外的成分来克服Vlasov-Poisson-Landau系统中存在的特定数学难题：提出了一种新的电势指数权值来抵消速度的增长，一种新的速度权值来捕捉朗道核中的弱速度扩散，一种新的电场衰减来关闭能量估计，以及一种新的自举参数来控制高矩和大振幅正则性的传播。
The classical Vlasov-Poisson-Landau system describes dynamics of a collisional plasma interacting with its own electrostatic eld as well as its grazing collisions. Such grazing collisions are modeled by the famous Landau (Fokker-Planck) collision kernel, proposed by Landau in 1936. We construct global unique solutions to such a system for initial data which have small weighted H norms, but can have large H(k 3) norms with high velocity moments. Our construction is based on accumulative study on the Landau kernel in the past decade [G1] [SG1-3], with four extra ingredients to overcome the speci c mathematical di¢ culties present in the Vlasov-Poisson-Landau system: a new exponential weight of electric potential to cancel the growth of the velocity, a new velocity weight to capture the weak velocity di¤usion in the Landau kernel, a decay of the electric eld to close the energy estimate, and a new bootstrap argument to control the propagation of the high moments and regularity with large amplitude.