Focusing intercritical NLS with inverse-square potential.

We study the focusing nonlinear Schrödinger equation with inverse-square potential i ∂ t u + Δ u − a | x | 2 u + | u | p − 1 u = 0 with a > − 1 4 and 3 4 < p − 1 < 4 in three dimensions. In this paper we obtain blow-up and global existence criteria for the solution to ( N L S a ) by the method from Duyckaerts-Roudenko [1], which extend a recent work of Killip-Murphy-Visan-Zheng [2] to above the threshold. [ABSTRACT FROM AUTHOR]