Regularity of the Boltzmann equation in convex domains
Regularity of the Boltzmann equation in convex domains
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DOI：
10.1007/s00222-016-0670-8
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发表时间：
2012-12
影响因子：
3.1
通讯作者：
Yan Guo;Chanwoo Kim;D. Tonon;A. Trescases
中科院分区：
文献类型：
--
作者：
Yan Guo;Chanwoo Kim;D. Tonon;A. Trescases
由于边界的特性以及碰撞算子的非局部混合，在物理边界条件下玻尔兹曼解的正则性的一个基本问题一直是开放的。考虑严格凸区域上的Boltzmann方程，其边界条件为镜面反射、反弹和漫射。借助于一个到掠集的距离函数，我们构造了所有边界条件的远离掠集的加权经典解。对于扩散边界条件，我们构造了的解，也构造了的加权解。
A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the Boltzmann equation in a strictly convex domain with the specular, bounce-back and diffuse boundary condition. With the aid of a distance function toward the grazing set, we construct weighted classicalsolutions away from the grazing set for all boundary conditions. For the diffuse boundary condition, we constructsolutions forand weightedsolutions foras well.