Uniqueness and cylindrical symmetry of ground states for magnetic nonlinear Choquard equation

Abstract This paper investigates ground states of the following magnetic nonlinear Choquard equation: − Δ A u + V ( x ) u = μ u + ( I 2 ∗ | u | 2 ) u in R 3 , where u ∈ H 1 ( R 3 , C ) satisfies ‖ u ‖ 2 2 = m > 0 , V ( x ) ∈ L ∞ ( R 3 ) , I 2 := 1 4 π | x | is the Riesz potential and Δ A denotes the magnetic Laplacian. By considering the associated constrained minimisation problem e A ( m ) , we prove the existence of ground states by employing the concentration compactness principle. Furthermore, we provide a refined description of the asymptotic behaviour of ground states as