Asymptotic profiles of blow-up solutions of the nonlinear Schrödinger equation with critical power nonlinearity (Q1890894)

The nonlinear Schrödinger equation \[ 2i {\partial u \over \partial t} + \Delta u + |u |^{p - 1} u = 0, \quad (t,x) \in\mathbb{R}_+ \times\mathbb{R}^N \tag{1} \] arises in various domains of physics. The number \(p = 1 + 4/N\) is the critical number for the existence of blow-up solutions of (1). This article deals with this critical case. A singular solution of (1) is studied.