Dynamics of the Critical Choquard Equation With a Focusing Local Perturbation

ABSTRACT In this paper, we study the following energy‐critical Choquard equation with a focusing local perturbation where , , , and is the Riesz potential of order . The existence and qualitative properties of the ground states for this problem have been well studied recently. However, the long‐time dynamics of solutions remain unknown. By employing the concentration‐compactness and rigidity method introduced by C. E. Kenig and F. Merle (Invent. Math., 166 (2006)), we establish a scattering vs. blow‐up dichotomy for radial solutions below the ground state energy threshold.