Global well-posedness and scattering for nonlinear Schrödinger equations with algebraic nonlinearity when $d = 2,3$ and $u_0$ is radial

In this paper we discuss global well-posedness and scattering for some initial value problems that are $\dot{H}^1$ subcritical. We prove global well-posedness and scattering for radial data in $H^s , s \gt s_c$, where the initial value problem is $\dot{H}^{s_c}$-critical. We make use of the long time Strichartz estimates of [13] to do this.

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During the time of writing this paper, the author was supported by an NSF postdoc, as well as NSF grants DMS-1500424 and DMS-1764358. The author was also a member of the Institute for Advanced Study as a von Neumann fellow during part of the writing of this paper. Finally, the author would like to acknowledge the helpful suggestions of the anonymous referee.

Received 3 May 2017

Published 11 September 2019