The radial defocusing nonlinear Schrödinger equation in three space dimensions

Abstract

We study the defocusing nonlinear Schrödinger equation in three space dimensions. We prove that any radial solution that remains bounded in the critical Sobolev space must be global and scatter. In the energy-supercritical setting, we employ a space-localized Lin--Strauss Morawetz inequality of Bourgain. In the inter-critical regime, we prove long-time Strichartz estimates and frequency-localized Lin--Strauss Morawetz inequalities.

37 pages

References in corpus (2)

• A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation
• Global well-posedness and scattering for the defocusing cubic NLS in four dimensions

Cited by in corpus (6)

• The radial defocusing energy-supercritical NLS in dimension four
• Two minimization problems on non-scattering solutions to mass-subcritical nonlinear Schrödinger equation
• Scattering theory for the radial ${\dot{H}}^{1/2}$-critical wave Equation with a cubic convolution
• Global well-posedness and scattering for nonlinear Schr{ö}dinger equations with algebraic nonlinearity when $d=2,3$, $u_0$ radial
• The defocusing quintic NLS in four space dimensions
• Scattering for the defocusing, cubic nonlinear Schr{ö}dinger equation with initial data in a critical space