Nonlinear smoothing and unconditional uniqueness for the Benjamin–Ono equation in weighted Sobolev spaces. (April 2021)

• Record Type: Journal Article
• Authors: Correia, Simão
• Is Part Of: Nonlinear analysis. Volume 205(2021)
• Publication Date: 2021-04
• Subjects: 35Q35 -- 35A02 -- 35B65 -- 42B37; Benjamin–Ono equation -- Nonlinear smoothing -- Unconditional uniqueness; 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.2020.112227
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider the Benjamin–Ono equation on the real line for initial data in weighted Sobolev spaces. After the application of the gauge transform, the flow is shown to be Lipschitz continuous and to present a nonlinear smoothing effect. As a consequence, unconditional uniqueness for the Benjamin–Ono equation is proved.