Analysis & PDE
- Anal. PDE
- Volume 5, Number 5 (2012), 913-960.
Two-dimensional nonlinear Schrödinger equation with random radial data
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 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.
Anal. PDE, Volume 5, Number 5 (2012), 913-960.
Received: 16 November 2010
Revised: 14 February 2011
Accepted: 3 June 2011
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 37L40: Invariant measures 37L50: Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systems
Secondary: 37K05: Hamiltonian structures, symmetries, variational principles, conservation laws
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