Scattering of the energy-critical NLS with inverse square potential

Abstract

We consider the initial value problem of the energy critical nonlinear Schrödinger equation with an inverse square potential in dimension d=4,5,6. In the focusing case, we achieve the global well-posedness and scattering when the kinetic energy and energy of the solution are both below the threshold of the ground state solution. In the defocusing case, we prove that any H˙1 bounded initial data leads to the global and scattering solution. No radial assumption is made on the initial data.