Global existence of L2 solutions to the Zakharov equations with additive noises. (April 2022)

• Record Type: Journal Article
• Authors: Tsutsumi, Yoshio
• Is Part Of: Nonlinear analysis. Volume 217(2022)
• Publication Date: 2022-04
• Subjects: Zakharov equations with additive noise -- Global existence of solutions -- Fourier restriction norm method; 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.2021.112709
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We show the global existence of L 2 solutions for the Cauchy problem of the Zakharov equations with additive noises in one spatial dimension. For the proof, we use the argument by Colliander, Holmer and Tzirakis, which was applied to the deterministic Zakharov equations. Our proof is an extension of their proof to the problem with stochastic external forces.