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

Zhang, JunyongZheng, Jiqiang2016-06-140022-1236http://hdl.handle.net/1885/103478We 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).Scattering theory for nonlinear Schr?dinger equations with inverse-square potential201410.1016/j.jfa.2014.08.0122016-06-14