Scattering theory for nonlinear Schr?dinger equations with inverse-square potential

Abstract

We study the long-time behavior of solutions to nonlinear Schrödinger equations with some critical rough potential of a|x| −2 type. The new ingredients are the interaction Morawetz-type inequalities and Sobolev norm property associated with Pa = −Δ + a|x|−2. We use such properties to obtain the scattering theory for the defocusing energysubcritical nonlinear Schrödinger equation with inverse square potential in energy space H1(Rn). Show more