The Gelfand-Shilov smoothing effect for the radially symmetric homogeneous Landau equation with Shubin initial datum
The Gelfand-Shilov smoothing effect for the radially symmetric homogeneous Landau equation with Shubin initial datum
复制标题
Shubin初始基准径向对称齐次Landau方程的Gelfand-Shilov平滑效应
DOI：
10.1016/j.crma.2018.04.022
复制
发表时间：
2018
影响因子：
0.8
通讯作者：
Li Hao Guang
中科院分区：
文献类型：
--
作者：
Li Hao Guang
本文研究了带有麦克斯韦分子的径向对称空间齐次非截止朗道方程的柯西问题，初始数据属于负指数Shubin空间，该空间可以用谐振子的谱分解来刻画。在此谱分解的基础上，利用Shubin类初值构造了该Cauchy问题的弱解，并证明了其解的唯一性和Gelfand-Shilov光滑效应.
In this paper, we study the Cauchy problem associated with the radially symmetric spatially homogeneous non-cutoff Landau equation with Maxwellian molecules, while the initial datum belongs to negative-index Shubin space, which can be characterized by spectral decomposition of the harmonic oscillators. Based on this spectral decomposition, we construct the weak solution with Shubin’s class initial datum, and then we prove the uniqueness and the Gelfand–Shilov smoothing effect of the solution to this Cauchy problem.