Global well-posedness and instability of an inhomogeneous nonlinear   Schrodinger equation with harmonic potential
  This paper is concerned with the Cauchy problem for an inhomogeneous nonlinear Schrodinger equation with exponential growth nonlinearity and harmonic potential in two space dimensions. We prove global well-posedness, existence of the associated ground state and instability of the standing wave. 
T. Saanouni
math.AP