Scattering for H^1/2 bounded solutions to the cubic, defocusing NLS in 3 dimensions

Abstract

We show that if a solution of the defocusing cubic NLS in 3d remains bounded in the homogeneous Sobolev norm of order 1/2 in its maximal interval of existence, then the interval is infinite and the solution scatters. No radial assumption is made.

To appear, Tran.Amer.Math.Soc

References in corpus (1)

• A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation

Cited by in corpus (4)

• Global wellposedness and scattering for the focusing energy-critical nonlinear Schrodinger equations of fourth order in the radial case
• The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher
• Energy-supercritical NLS: critical ${\dot{H}}^s$-bounds imply scattering
• Numerical simulations of the energy- supercritical Nonlinear Schrödinger equation