Modified Strichartz estimates with an application to the critical nonlinear Schrödinger equation. (January 2016)

• Record Type: Journal Article
• Authors: Nakamura, Makoto; Wada, Takeshi
• Is Part Of: Nonlinear analysis. Volume 130(2015)
• Page Start: 138
• Page End: 156
• Publication Date: 2016-01
• Subjects: primary 35Q55 -- secondary 35Q41; Nonlinear Schrödinger equation -- Strichartz estimate -- Cauchy problem -- Sobolev space; 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.2015.09.023
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The Cauchy problem for the critical nonlinear Schrödinger equation is considered in the Sobolev space of fractional order. Some modified Strichartz estimates are constructed and applied to the problem to obtain small global solutions with less regularity assumption for the nonlinear term.