Almost sure scattering for the nonlinear Klein–Gordon equations with Sobolev critical power. (April 2022)

• Record Type: Journal Article
• Authors: Chen, Jie; Wang, Baoxiang
• Is Part Of: Nonlinear analysis. Volume 217(2022)
• Publication Date: 2022-04
• Subjects: Nonlinear Klein–Gordon equation -- Probabilistic scattering -- Wave packet decomposition; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112732
• Languages: English
• ISSNs: 0362-546X

Abstract

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.