论文标题
紧凑型谎言组的漂移扩散方程与分数扩散
Drift diffusion equations with fractional diffusion on compact Lie groups
论文作者
论文摘要
在这项工作中，我们研究了紧凑型谎言基团上与伪伪差异算子相关的扩散方程的适当性。强烈的椭圆运算符的扩散被认为是一种特殊情况，尤其是相对于拉普拉斯式的分数扩散。在与该组的次摩曼结构相关的Hörmander类中研究了一般案例（由矢量字段的Hörmander系统编码）。研究了针对分数亚拉普拉斯人的扩散方程，更一般的子细胞运算符的分数功率以及带有漂移$ D $的相应的准地藻模型。 SU（2）的示例分析了分数扩散问题的示例。
In this work we investigate the well-posedness for difussion equations associated to subelliptic pseudo-differential operators on compact Lie groups. The diffusion by strongly elliptic operators is considered as a special case and in particular the fractional diffusion with respect to the Laplacian. The general case is studied within the Hörmander classes associated to a sub-Riemannian structure on the group (encoded by a Hörmander system of vector fields). Applications to diffusion equations for fractional sub-Laplacians, fractional powers of more general subelliptic operators, and the corresponding quasi-geostrophic model with drift $D$ are investigated. Examples on SU(2) for diffusion problems with fractional diffusion are analysed.
