Document Type

Article

Publication Date

4-1-2023

Abstract

We establish quantitative blow-up criteria below the scaling threshold for radially symmetric solutions to the defocusing nonlinear Schrödinger equation with nonlinearity |u|6 u. This provides to our knowledge the first generic results distinguishing potential blow-up solutions of the defocusing equation from many of the known examples of blow-up in the focusing case. Our main tool is a quantitative version of a result showing that uniform bounds on L2-based critical Sobolev norms imply scattering estimates. As another application of our techniques, we establish a variant which allows for slow growth in the critical norm. We show that if the critical Sobolev norm on compact time intervals is controlled by a slowly growing quantity depending on the Strichartz norm, then the solution can be extended globally in time, with a corresponding scattering estimate.

Publication Source (Journal or Book title)

American Journal of Mathematics

First Page

543

Last Page

567

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