Exponential Decay for Soft Potentials near Maxwellian
Exponential Decay for Soft Potentials near Maxwellian
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DOI：
10.1007/s00205-007-0067-3
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发表时间：
2008-02
影响因子：
2.5
通讯作者：
Robert M. Strain;Yan Guo
中科院分区：
文献类型：
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作者：
Robert M. Strain;Yan Guo
我们在周期盒中考虑角截断软势和玻尔兹曼理论中的朗道碰撞核。我们证明了对于λ > 0和0 <p< 1，在给定的麦克斯韦函数附近的任何光滑扰动都以的速率趋近于零。我们的方法是基于一个统一的能量估计与适当的指数速度权重。我们的结果推广了经典的Caflischof [2]的结果到非常软的势和库仑相互作用的情形，并且改进了[5，14]最近的“几乎指数”衰减结果.
We consider both soft potentials with angular cutoff and Landau collision kernels in the Boltzmann theory inside a periodic box. We prove that any smooth perturbation near a given Maxwellian approaches zero at the rate offor some λ > 0 and 0 <p< 1. Our method is based on an unified energy estimate with appropriate exponential velocity weight. Our results extend the classical resultCaflischof [2] to the case of very soft potential and Coulomb interactions, and also improve the recent “almost exponential” decay results by [5, 14].