On the well-posedness for the nonlinear radial Schrödinger equation with spatial variable coefficients. (May 2019)

• Record Type: Journal Article
• Authors: Zheng, Bo-wen
• Is Part Of: Nonlinear analysis. Volume 182(2019)
• Page Start: 1
• Page End: 19
• Publication Date: 2019-05
• Subjects: 35B65 -- 35Q40 -- 35Q55; Schrödinger equation with spatial variable coefficients -- Strichartz estimate -- Weighted Sobolev space -- Well-posedness; 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.2018.11.016
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study the Cauchy problem for a generalized nonlinear Schrödinger equation with spatial variable coefficients. A new weighted Sobolev space W 1, q ( R + ) is introduced and the range of admissible pairs for the Strichartz estimates is improved. As an application, we show the local well-posedness result for the initial data in W 1, q ( R + ) .