Focusing NLS with inverse square potential

Source abstract

In this paper, we utilize Dodson-Murphy’s method to establish the radial scattering result for the focusing nonlinear Schrödinger equation with inverse square potential i∂tu−Lau=−|u|p−1u in the energy space Ha1(Rd) in dimensions d ≥ 3, which extends our previous result to higher dimensional cases but with radial initial data. The new ingredient is to establish the dispersive estimate for radial functions and overcome the weak dispersive estimate when a < 0.