Nonlinear Schrödinger equations with coupled Hartree-type terms and rotation

Abstract

We consider the Cauchy problem for a class of magnetic Schrödinger system with local and nonlocal nonlinearities. The problem stems from a typical model describing the meanfield dynamics of rotating many-body bosons in a confining trap. We present sufficient conditions which yield global well-posedness or finite time blowup solutions to the system.

Orbital stability of standing waves for supercritical NLS with potential on graphs

“…We refer the readers to [18] for a rigorous derivation in the stationary case of (1.1). Recently, the equation (1.1) has attracted attentions due to their significance in theory and applications, see [1][2][3]5,6,8,14,17] and references therein. Antonelli et al in [2] proved existence and uniqueness of the Cauchy problem.…”