Blow-up for the 3D intercritical inhomogeneous NLS with inverse-square potential

Abstract

In this paper we study the focusing inhomogeneous 3D nonlinear Schrödinger equation with inverse-square potential in the mass-supercritical and energy-subcritical regime. We first establish local well-posedness in ${\dot{H}}_a^{s_c}\cap {\dot{H}}_a^1$, with $s_c=3/2-(2-b)/2\sigma$. Next, we prove the blow-up of the scaling invariant Lebesgue norm for radial solutions and also, with an additional restriction, in the non-radial case.

21 pages