On the life span of the Schrödinger equation with sub-critical power nonlinearity (Q1032711)

The life span \(T(\varepsilon)\) of the Cauchy problem for the one-dimensional Schrödinger equation with a single power nonlinearity \(\lambda|u|^{p-1}u\) \((\lambda\in{C}, 2\leq p<3)\) and inital data \(\varepsilon\varphi\) (of size \(\varepsilon\) with \(\varphi\) belonging to a suitable function space) is discussed. The main result is Theorem 1.1 wherein a precise lower bound for \(\liminf_{\varepsilon\to0}\varepsilon^{2(p-1)/(3-p)}T(\varepsilon)\) is given.