Global well-posedness and scattering for the defocusing cubic NLS in four dimensions

Abstract

In this short note we present a new proof of the global well-posedness and scattering result for the defocusing energy-critical NLS in four space dimensions obtained previously by Ryckman and Visan. The argument is inspired by the recent work of Dodson on the mass-critical NLS.

References in corpus (6)

• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
• The cubic nonlinear Schrödinger equation in two dimensions with radial data
• Energy-supercritical NLS: critical ${\dot{H}}^s$-bounds imply scattering
• Global well-posedness and scattering for the mass-critical nonlinear Schrödinger equation for radial data in high dimensions
• Scattering for the cubic Klein--Gordon equation in two space dimensions

Cited by in corpus (9)

• The radial defocusing nonlinear Schrödinger equation in three space dimensions
• The radial defocusing energy-supercritical NLS in dimension four
• The Defocusing Energy-Critical Wave Equation with a Cubic Convolution
• Global well-posedness and scattering for the defocusing, energy -critical, nonlinear Schr{ö}dinger equation in the exterior of a convex obstacle when $d=4$
• Large time behavior in nonlinear Schrodinger equation with time dependent potential
• Inter-critical NLS: critical ${\dot{H}}^s$-bounds imply scattering
• Global well-posedness and scattering for the defocusing quintic NLS in three dimensions
• Well-posedness for energy-critical nonlinear Schrödinger equation on waveguide manifold
• Global Well-Posedness of 2D Non-Focusing Schrödinger Equations via Rigorous Modulation Approximation