论文标题
在空间上不均匀的Landau方程的分析平滑效应对硬电位
Analytic smoothing effect of the spatially inhomogeneous Landau equations for hard potentials
论文作者
论文摘要
我们研究了在扰动环境中具有硬潜力的空间不均匀兰道方程，并在空间和速度变量中建立了一类低规度弱解决方案的分析平滑效应。这表明Landau方程式基本上是fokker-Planck操作员。空间分析性依赖于新的时间平均运算符，并且证明基于直接的能量估计，并仔细估算了有关新的时间平均操作员的衍生产品。
We study the spatially inhomogeneous Landau equations with hard potential in the perturbation setting, and establish the analytic smoothing effect in both spatial and velocity variables for a class of low-regularity weak solutions. This shows the Landau equations behave essentially as the hypoelliptic Fokker-Planck operators. The spatial analyticity relies on a new time-average operator, and the proof is based on a straightforward energy estimate with a careful estimate on the derivatives with respect to the new time-average operator.
