On short-time bilinear Strichartz estimates and applications to the Shrira equation. (September 2020)

• Record Type: Journal Article
• Authors: Schippa, Robert
• Is Part Of: Nonlinear analysis. Volume 198(2020)
• Publication Date: 2020-09
• Subjects: Dispersive equations -- Shrira equation -- Bilinear strichartz estimates -- Energy method -- Short-time Fourier restriction spaces; 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.2020.111910
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Short-time bilinear Strichartz estimates for Schrödinger-like equations on tori are proved, which resemble the bilinear Strichartz estimates on Euclidean space. By this and a known combination of perturbative and energy arguments, we improve the well-posedness theory for the Shrira equation.