Decay of the linearized Boltzmann-Vlasov system
Decay of the linearized Boltzmann-Vlasov system
复制标题
线性玻尔兹曼-弗拉索夫系统的衰变
DOI：
10.1080/00411459908205653
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发表时间：
1999
影响因子：
--
通讯作者：
W. Strauss
中科院分区：
文献类型：
--
作者：
R. Glassey;W. Strauss
摘要在线性化情况下研究了包含玻尔兹曼碰撞的相对论等离子体的运动。将具有Boltzmann碰撞算子的Vlasov-Poisson系统线性化为具有周期边界条件的全局Maxwell系统。在适当的散射核假设下，证明了线性化方程的任意解在t → ∞时以全局L2范数指数衰减，即线性化意义下的Maxwell方程是渐近稳定的.对于具有相同边界条件的完全非线性问题，也证明了全局Maxwell在L1中是稳定的。
Abstract The motion of relativistic plasma including Boltzmann-type collisions is studied in the linearized situation. The Vlasov-Poisson system with a Boltzmann collision operator is linearized around a global Maxwellian with periodic boundary conditions in the space variable. Under appropriate assumptions on the scattering kernel, it is shown that any solution to this linearized equation decays exponentially in a global L 2-norm as t → ∞; that is, the Maxwellian is asymptotically stable in the linearized sense. For the full nonlinear problem with the same boundary conditions, it is also shown that the global Maxwellian is stable in L 1.