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2012 Two-dimensional nonlinear Schrödinger equation with random radial data
Yu Deng
Anal. PDE 5(5): 913-960 (2012). DOI: 10.2140/apde.2012.5.913

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.

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Yu Deng. "Two-dimensional nonlinear Schrödinger equation with random radial data." Anal. PDE 5 (5) 913 - 960, 2012. https://doi.org/10.2140/apde.2012.5.913

Information

Received: 16 November 2010; Revised: 14 February 2011; Accepted: 3 June 2011; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1264.35212
MathSciNet: MR3022846
Digital Object Identifier: 10.2140/apde.2012.5.913

Subjects:
Primary: 35Q55, 37L40, 37L50
Secondary: 37K05

Rights: Copyright © 2012 Mathematical Sciences Publishers

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