The Cauchy problem for the inhomogeneous non-cutoff Kac equation in critical Besov space
The Cauchy problem for the inhomogeneous non-cutoff Kac equation in critical Besov space
复制标题
临界Besov空间中非齐次非截止Kac方程的柯西问题
DOI：
10.1016/j.jde.2019.12.025
复制
发表时间：
2020
影响因子：
2.4
通讯作者：
Xu Jiang
中科院分区：
文献类型：
--
作者：
Cao Hong-Mei;Li Hao-Guang;Xu Chao -Jiang;Xu Jiang
In this work, we investigate the Cauchy problem for the spatially inhomogeneous non-cutoff Kac equation. If the initial datum belongs to the spatially critical Besov space, we can prove the well-posedness of weak solution under a perturbation framework. Furthermore, it is shown that the solution enjoys Gelfand-Shilov regularizing properties with respect to the velocity variable and Gevrey regularizing properties with respect to the position variable. In comparison with the recent result in [18], the Gelfand-Shilov regularity index is improved to be optimal. To the best of our knowledge, our work is the first one that exhibits smoothing effect for the kinetic equation in Besov spaces.
