Dynamics of the Critical Choquard Equation With a Focusing Local Perturbation
Abstract
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.
Fields of Study & Subjects
Advanced Mathematical Physics Problems
Nonlinear Partial Differential Equations
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Mathematical Methods in the Applied Sciences
- Volume
- 49
- Issue
- 9
- Pages
- 9246–9287
- Publication date
- 29 January 2026
- Language
- EN