Sharp weights in the Cauchy problem for nonlinear Schrodinger equations   with potential
  We review different properties related to the Cauchy problem for the (nonlinear) Schrodinger equation with a smooth potential. For energy-subcritical nonlinearities and at most quadratic potentials, we investigate the necessary decay in space in order for the Cauchy problem to be locally (and globally) well-posed. The characterization of the minimal decay is different in the case of super-quadratic potentials. 
R\'emi Carles (I3M)
math.AP math-ph math.MP