## Analysis & PDE

• Anal. PDE
• Volume 5, Number 5 (2012), 913-960.

### Two-dimensional nonlinear Schrödinger equation with random radial data

Yu Deng

#### Abstract

We study radial solutions of a certain two-dimensional nonlinear Schrödinger (NLS) equation with harmonic potential, which is supercritical with respect to the initial data. By combining the nonlinear smoothing effect of Schrödinger equation with $Lp$ estimates of Laguerre functions, we are able to prove an almost-sure global well-posedness result and the invariance of the Gibbs measure. We also discuss an application to the NLS equation without harmonic potential.

#### Article information

Source
Anal. PDE, Volume 5, Number 5 (2012), 913-960.

Dates
Revised: 14 February 2011
Accepted: 3 June 2011
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.apde/1513731261

Digital Object Identifier
doi:10.2140/apde.2012.5.913

Mathematical Reviews number (MathSciNet)
MR3022846

Zentralblatt MATH identifier
1264.35212

#### Citation

Deng, Yu. Two-dimensional nonlinear Schrödinger equation with random radial data. Anal. PDE 5 (2012), no. 5, 913--960. doi:10.2140/apde.2012.5.913. https://projecteuclid.org/euclid.apde/1513731261

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