Blowup Dynamics of the Focusing Energy-critical Hartree Equation

Abstract

This paper is concerned with blowup dynamics of the focusing energy-critical Hartree equation in dimensions five and higher. We prove that if the kinetic energy of a blowup solution is bounded, it must concentrate at least the kinetic energy of the ground state as time goes to the blowup time. Finally, we also show that the finite time blowup solution has a limit in some suitable spaces.