The defocusing quintic NLS in four space dimensions

Abstract

We consider the defocusing quintic nonlinear Schrödinger equation in four space dimensions. We prove that any solution that remains bounded in the critical Sobolev space must be global and scatter. We employ a space-localized interaction Morawetz inequality, the proof of which requires us to overcome the logarithmic failure in the double Duhamel argument in four dimensions.

29 pages

References in corpus (3)

• A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation
• Global well - posedness and scattering for the focusing, energy - critical nonlinear Schrödinger problem in dimension $d=4$ for initial data below a ground state threshold
• The radial defocusing nonlinear Schrödinger equation in three space dimensions

Cited by in corpus (2)

• On scattering for the defocusing nonlinear Schrödinger equation on waveguide ${\mathbb{R}}^m$ $\times$ $\mathbb{T}$ (when $m=2,3$)
• Global well-posedness and scattering for the defocusing cubic Schrödinger equation on waveguide ${\mathbb{R}}^2$ $\times$ ${\mathbb{T}}^2$