Regularity of Stationary Solutions to the Linearized Boltzmann Equations
Regularity of Stationary Solutions to the Linearized Boltzmann Equations
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DOI：
10.1137/16m1099844
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发表时间：
2016-04
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影响因子：
--
通讯作者：
I-Kun Chen
中科院分区：
文献类型：
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作者：
I-Kun Chen
本文研究了具有截止硬势和截止Maxwell气体的线性Boltzmann方程在$\mathbb{R}^3$中有界C^1 $凸区域上定态解的正则性.我们证明了当输入数据具有相同的正则性时，定态解是H\"{o}lder连续的，且离边界的阶数为$\frac1{2}^-$.其核心思想是通过输运和碰撞将碰撞获得的速度规律性部分转移到空间。
We consider the regularity of stationary solutions to the linearized Boltzmann equations in bounded $C^1$ convex domains in $\mathbb{R}^3$ for gases with cutoff hard potential and cutoff Maxwellian gases. We prove that the stationary solutions solutions are H\"{o}lder continuous with order $\frac1{2}^-$ away from the boundary provided the incoming data have the same regularity. The key idea is to partially transfer the regularity in velocity obtained by collision to space through transport and collision.