Strong instability of standing waves for the Hartree equation with a constant magnetic field

In this paper, we study the strong instability of standing waves for the Hartree equation with a constant magnetic field. First, we prove the existence of least action ground states for the associated stationary equation using variational methods. Second, by establishing the approximation relation between the rescaled stationary magnetic Hartree equation and the classical Hartree equation, we prove the strong instability of least action ground state standing waves with positive angular momentum at sufficiently large frequencies in L 2 -supercritical case.