Almost sure scattering for the nonlinear Klein–Gordon equations with Sobolev critical power. (April 2022) - Chen, Jie; Wang, Baoxiang
Abstract: 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 × H s − 1, 3 d − 1 4 ( d − 1 ) < s < 1 for 4 ≤ d ≤ 6 . We use the induction on scales and bushes argument in Bringmann (2018) where the model equation is wave equation. For d = 5, 6, 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.