Blow-up solutions of the intercritical inhomogeneous NLS equation: the non-radial case

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 Ḣsc a ∩ Ḣ1 a , with sc = 3/2 − (2 − b)/2σ. 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.