Scattering of the focusing energy-critical NLS with inverse square potential in the radial case

Abstract

<p style='text-indent:20px;'>We consider the Cauchy problem of the focusing energy-critical nonlinear Schrödinger equation with an inverse square potential. We prove that if any radial solution obeys the supreme of the kinetic energy over the maximal lifespan is below the kinetic energy of the ground state solution, then the solution exists globally in time and scatters in both time directions.