Two Dimensional NLS Equation With Random Radial Data

Abstract

In this paper we study radial solutions of certain two-dimensional nonlinear Schrödinger equation with harmonic potential, which is supercritical with respect to the initial data. By combining the nonlinear smoothing effect of Schr ödinger 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.

References in corpus (3)

• Almost sure well-posedness of the cubic nonlinear Schrödinger equation below L^2(T)
• A pseudoconformal compactification of the nonlinear Schrödinger equation and applications
• Invariant Gibbs Measures and a.s. Global Well-Posedness for Coupled KdV Systems

Cited by in corpus (1)

• Quasi-invariant gaussian measures for one dimensional Hamiltonian PDE's