Solution to the stochastic Schrödinger equation on the full space. (4th March 2019)

• Record Type: Journal Article
• Authors: Debussche, Arnaud; Martin, Jörg
• Is Part Of: Nonlinearity. Volume 32:Number 4(2019)
• Page Start: 1147
• Page End: 1174
• Publication Date: 2019-03-04
• Subjects: nonlinear Schrödinger equation -- localization -- white noise -- renormalization; 60H15 -- 35Q55; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aaf50e
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We show here how the methods recently applied in Debussche and Weber (2018 Electron. J. Probab . 23 28) to solve the stochastic nonlinear Schrödinger equation on can be enhanced to yield solutions on if the nonlinearity is weak enough. We prove that the solutions remain localized on compact time intervals which allow us to apply energy methods on the full space.