Blow-up solutions of inhomogeneous nonlinear Schrödinger equations

In this paper, we study blow-up solutions to the Cauchy problem of the inhomogeneous nonlinear Schrodinger equation $$ \partial_t u = i ( f(x) \Delta u + \nabla f(x) \cdot \nabla u +k(x)|u|^2u) $$ on \({\mathbb{R}}^2\). We present existence and non-existence results and investigate qualitative properties of the solutions when they exist.