On a Class of Inhomogeneous, Energy-Critical, Focusing, Nonlinear Schrödinger Equations

In this paper, we study the Cauchy problem of the inhomogeneous energy-critical Schrödinger equation: . Using the potential well method, we establish some new sharp criteria for blow-up of solutions in the nonradial case. In particular, our conclusion in some sense improves on the results in [Kenig and Merle, Invent. Math. 166, 645-675 (2006)], where only the radial case is considered in dimensions 3, 4, 5.