Global existence and blowup for Choquard equations with an inverse-square potential

Abstract

In this paper, the Choquard equation with an inverse-square potential and both focusing and defocusing nonlinearities in the energy-subcritical regime is investigated. For all the cases, the local well-posedness result in $H^1({\mathbb{R}}^N)$ is established. Moreover, the global existence result for arbitrary initial values is proved in the defocusing case while a global existence/blowup dichotomy below the ground state is established in the focusing case.

References in corpus (1)

• Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data