论文标题
具有Sobolev临界功率的非线性klein-gordon方程的几乎确定散射
Almost sure scattering for the nonlinear Klein-Gordon equations with Sobolev critical power
论文作者
论文摘要
在本文中，我们研究了具有Sobolev临界功率的Klein-Gordon方程的几乎确定的散射。我们在$ H^S \ times H^{s-1} $中获得具有随机初始数据的几乎确定的散射； $ 11/12 <s <1 $ for $ d = 4 $，$ 15/16 <s <1 $ for $ d = 5 $。我们在[9]中使用量表和灌木参数的诱导，其中模型方程是波动方程。对于d = 5，我们使用klein-gordon方程的质量项来控制尺度诱导过程中能量增量的控制。
In this paper, we study the almost sure scattering for the Klein-Gordon equations with Sobolev critical power. We obtain the almost sure scattering with random initial data in $H^s \times H^{s-1}$; $11/12 < s < 1$ for $d = 4$, $15/16 < s < 1$ for $d = 5$. We use the induction on scales and bushes argument in [9] where the model equation is wave equation. For d = 5, we use the mass term of the Klein-Gordon equation to obtain the control of the increment of energy in the process of induction on scales.
