Rate of $L^2$-concentration of the blow-up solutionfor critical nonlinear Schrödinger equation with potential

Jian Zhang; Shihui Zhu; Xiaoguang Li

doi:10.3934/mcrf.2011.1.119

Article Contents

2011, Volume 1, Issue 1: 119-127. Doi: 10.3934/mcrf.2011.1.119

This issue Previous Article A deterministic linear quadratic time-inconsistent optimal control problem Next Article

Rate of $L^2$-concentration of the blow-up solution for critical nonlinear Schrödinger equation with potential

1.
College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068
2.
College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066
3.
College of Economics, Sichuan Normal University, Chengdu 610066

Received: September 30, 2010

Revised: December 31, 2010

Published: February 2011

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Abstract

We consider the blow-up solutions of the Cauchy problem for the critical nonlinear Schrödinger equation with a repulsive harmonic potential. In terms of Merle and Tsutsumi's arguments as well as Carles' transform, the $L^2$-concentration property of radially symmetric blow-up solutions is obtained.

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Mathematics Subject Classification: Primary: 35Q55; Secondary: 35B44.

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References

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