Global well-posedness and scattering for nonlinear Schr{ö}dinger equations with algebraic nonlinearity when $d=2,3$, $u_0$ radial

Abstract

In this paper we discuss global well - posedness and scattering for some initial value problems that are $L^2$ supercritical and ${\dot{H}}^1$ subcritical, with radial data. We prove global well - posedness and scattering for radial data in $H^s$, $s>s_c$, where the problem is ${\dot{H}}^{s_c}$ - critical. We make use of the long time Strichartz estimates of \cite{D2} to do this.

38 pages

References in corpus (1)

• The radial defocusing nonlinear Schrödinger equation in three space dimensions

Cited by in corpus (4)

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• On the high-low method for NLS on the hyperbolic space
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• $H_x^s\times H_x^s$ scattering theory for a weighted gradient system of 3D radial defocusing NLS