LAUSR

Abstract We consider the initial value problem of the energy critical nonlinear Schrodinger 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.