Blowup and global existence of the nonlinear Schrödinger equations with multiple potentials

Zaihui Gan; Boling Guo; Jian Zhang

doi:10.3934/cpaa.2009.8.1303

Article Contents

2009, Volume 8, Issue 4: 1303-1312. Doi: 10.3934/cpaa.2009.8.1303

This issue Previous Article Systems of convex Hamilton-Jacobi equations with implicit obstacles and the obstacle problem Next Article Hyperbolic--parabolic singular perturbation for mildly degenerate Kirchhoff equations: Global-in-time error estimates

Blowup and global existence of the nonlinear Schrödinger equations with multiple potentials

1.
College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068
2.
Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088

Received: December 2007

Revised: August 2008

Published: July 2009

Abstract / Introduction Related Papers Cited by

Abstract

This paper is concerned with the Cauchy problem for the nonlinear Schrödinger equations with multiple potentials. Under some assumptions on these potentials, we first obtain some sufficient conditions of blowup according to the initial energy and the Cauchy initial data directly. We next establish a sufficient condition of global existence by using potential well method and the relation between the Cauchy data and the ground state. We finally answer the question that how small the Cauchy initial data need to be for global existence by using scaling argument.

Keywords:

Mathematics Subject Classification: Primary: 35A15, 35Q55; Secondary: 35B30.

Citation:

Article Metrics

HTML views() PDF downloads(79) Cited by(0)

Blowup and global existence of the nonlinear Schrödinger equations with multiple potentials

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Blowup and global existence of the nonlinear Schrödinger equations with multiple potentials

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content