## Differential and Integral Equations

- Differential Integral Equations
- Volume 19, Number 7 (2006), 761-771.

### Limit behavior of blow-up solutions for critical nonlinear Schrödinger equation with harmonic potential

#### 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.

#### Article information

**Source**

Differential Integral Equations, Volume 19, Number 7 (2006), 761-771.

**Dates**

First available in Project Euclid: 21 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356050348

**Mathematical Reviews number (MathSciNet)**

MR2235893

**Zentralblatt MATH identifier**

1212.35056

**Subjects**

Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Secondary: 35B40: Asymptotic behavior of solutions

#### Citation

Li, Xiaoguang; Zhang, Jian. Limit behavior of blow-up solutions for critical nonlinear Schrödinger equation with harmonic potential. Differential Integral Equations 19 (2006), no. 7, 761--771. https://projecteuclid.org/euclid.die/1356050348