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

Abstract

We consider the mass-subcritical nonlinear Schrödinger 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 $\Vert |x{|}^{|s_c|}{e}^{-it\hat{I}”}u{\Vert }_{L_t^{\infty }{L}_x^2}<\infty$ on its maximal interval of existence must be global and scatter.

29 pages