Global Well-posedness for Schrodinger Equations with Derivative in a Nonlinear Term and Data in Low-order Sobolev Spaces
Date
2001-06-05
Authors
Takaoka, Hideo
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
In this paper, we study the existence of global solutions to Schrodinger equations in one space dimension with a derivative in a nonlinear term. For the Cauchy problem we assume that the data belongs to a Sobolev space weaker than the finite energy space H1. Global existence for H1 data follows from the local existence and the use of a conserved quantity. For Hs data with s < 1, the main idea is to use a conservation law and a frequency decomposition of the Cauchy data then follow the method introduced by Bourgain [3]. Our proof relies on a generalization of the tri-linear estimates associated with the Fourier restriction norm method used in [1, 25].
Description
Keywords
Nonlinear Schrodinger equation, Well-posedness
Citation
Takaoka, H. (2001). Global well-posedness for Schrodinger equations with derivative in a nonlinear term and data in low-order Sobolev spaces. <i>Electronic Journal of Differential Equations, 2001</i>(42), pp. 1-23.
Rights
Attribution 4.0 International