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2006 Limit behavior of blow-up solutions for critical nonlinear Schrödinger equation with harmonic potential
Xiaoguang Li, Jian Zhang
Differential Integral Equations 19(7): 761-771 (2006).

Abstract

We consider the blow-up solutions of the Cauchy problem for the critical nonlinear Schrödinger equation with a harmonic potential $i\phi_t+\frac{1}{2}\bigtriangleup\phi- \frac{1}{2}\omega^2|x|^2\phi+|\phi|^{4/N}\phi=0,\quad x \in R^N,\quad t \geq 0,$ which models the Bose-Einstein condensate. We establish the lower bound of blow-up rate as $t\rightarrow T$. Furthermore, the $L^2-$concentration property of the radially symmetric blow-up solutions is obtained.

Citation

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Xiaoguang Li. Jian Zhang. "Limit behavior of blow-up solutions for critical nonlinear Schrödinger equation with harmonic potential." Differential Integral Equations 19 (7) 761 - 771, 2006.

Information

Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35056
MathSciNet: MR2235893

Subjects:
Primary: 35Q55
Secondary: 35B40

Rights: Copyright © 2006 Khayyam Publishing, Inc.

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Vol.19 • No. 7 • 2006
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