For radial data with energy just above the ground state, the energy-critical Hartree equation has a dichotomy: solutions scatter or blow up according to a sign functional, after at most one passage near the ground state.
Cazenave,Semilinear Schr¨ odinger equations
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Global dynamics above the ground state for the energy-critical Hartree equation with radial data
For radial data with energy just above the ground state, the energy-critical Hartree equation has a dichotomy: solutions scatter or blow up according to a sign functional, after at most one passage near the ground state.