数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (5): 1923-1938.doi: 10.1016/S0252-9602(11)60371-8

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ON THE CONCENTRATION PROPERTIES FOR THE NONLINEAR SCHRÖDINGER EQUATION WITH A STARK POTENTIAL

朱世辉1,2*|张健1   

  1. 1. Visual Computing and Virtual Reality Key Laboratory, Sichuan Normal University, Chengdu 610066, China;
    2. College of Mathematics, Sichuan University, Chengdu 610064, China
  • 收稿日期:2009-12-01 出版日期:2011-09-20 发布日期:2011-09-20
  • 通讯作者: ZHU Shi-Hui,zhu_shihui2008@163.com E-mail:zhu_shihui2008@163.com; zhangjiancdv@sina.com
  • 基金资助:

    This work supported by National Science Foundation of China (11071177). †Corresponding author: Zhu Shihui.

ON THE CONCENTRATION PROPERTIES FOR THE NONLINEAR SCHRÖDINGER EQUATION WITH A STARK POTENTIAL

 ZHU Shi-Hui1,2*, ZHANG Jian1   

  1. 朱世辉, zhu_shihui2008@163.com
  • Received:2009-12-01 Online:2011-09-20 Published:2011-09-20
  • Supported by:

    This work supported by National Science Foundation of China (11071177). †Corresponding author: Zhu Shihui.

摘要:

In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schr¨odinger equation with a Stark potential. Using the variational char-acterization of the ground state for nonlinear Schr¨odinger equation without any potential, we obtain some concentration properties of blow-up solutions, including that the origin is the blow-up point of the radial blow-up solutions, the phenomenon of L2-concentration and rate of L2-concentration of blow-up solutions.

关键词: nonlinear Schr¨odinger equation, blow-up solution, blow-up point, L2-concentration, concentration compact principle

Abstract:

In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schr¨odinger equation with a Stark potential. Using the variational char-acterization of the ground state for nonlinear Schr¨odinger equation without any potential, we obtain some concentration properties of blow-up solutions, including that the origin is the blow-up point of the radial blow-up solutions, the phenomenon of L2-concentration and rate of L2-concentration of blow-up solutions.

Key words: nonlinear Schr¨odinger equation, blow-up solution, blow-up point, L2-concentration, concentration compact principle

中图分类号: 

  • 35F25