On a Class of Nonlinear Schrödinger Equations with Nonnegative Potentials in Two Space Dimensions

This paper discusses a class of critical nonlinear Schrödinger equations which are closely related to several applications, in particular to Bose-Einstein condensates with attractive two-body interactions. By constructing a constrained variational problem and considering the so-called invariant manifolds of the evolution flow, the authors derive a sharp criterion for blow-up and global existence of the solutions.