Local and global well-posedness for dispersion generalized Benjamin–Ono equations on the circle. (July 2020)

• Record Type: Journal Article
• Authors: Schippa, Robert
• Is Part Of: Nonlinear analysis. Volume 196(2020)
• Publication Date: 2020-07
• Subjects: Dispersive equations -- Benjamin–Ono equation -- Short-time Fourier restriction norm method -- Modified energies; 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.2020.111777
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: New local well-posedness results for dispersion generalized Benjamin-Ono equations are proved in the periodic case. The family of equations under consideration links the Benjamin–Ono and Korteweg–de Vries equation. For sufficiently strong dispersion global well-posedness in L 2 ( T ) is derived.