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arXiv · 1606.01512

Large data mass-subcritical NLS: critical weighted bounds imply scattering

Rowan Killip·Satoshi Masaki·Jason Murphy·Monica Visan
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Abstract

We consider the mass-subcritical nonlinear Schr\"odinger equation in all space dimensions with focusing or defocusing nonlinearity. For such equations with critical regularity $s_c\in(\max\{-1,-\frac{d}{2}\},0)$, we prove that any solution satisfying $\|\, |x|^{|s_c|}e^{-it\Delta} u\|_{L_t^\infty L_x^2} <\infty$ on its maximal interval of existence must be global and scatter.

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Rowan Killip, Satoshi Masaki, Jason Murphy, Monica Visan. 2016-06-05. Large data mass-subcritical NLS: critical weighted bounds imply scattering. https://arxiv.org/abs/1606.01512

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