Non relativistic and ultra relativistic limits in 2D stochastic nonlinear damped Klein–Gordon equation. (6th June 2022)

• Record Type: Journal Article
• Authors: Fukuizumi, Reika; Hoshino, Masato; Inui, Takahisa
• Is Part Of: Nonlinearity. Volume 35:Number 6(2022)
• Page Start: 2878
• Page End: 2919
• Publication Date: 2022-06-06
• Subjects: damped nonlinear Klein–Gordon equation -- stochastic partial differential equations -- white noise -- non relativistic limit -- ultra relativistic limit; 35L71 -- 35A35 -- 60H15; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac64e0
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We study the non relativistic and ultra relativistic limits in the two-dimensional nonlinear damped Klein–Gordon equation driven by a space-time white noise on the torus. In order to take the limits, it is crucial to clarify the parameter dependence in the estimates of solution. In this paper we present two methods to confirm this parameter dependence. One is the classical, simple energy method. Another is the method via Strichartz estimates.