A sharp lower bound for the lifespan of small solutions to the Schrödinger equation with a subcritical power nonlinearity

Yuji Sagawa, Hideaki Sunagawa, Shunsuke Yasuda

Let $T_{\epsilon }$ be the lifespan for the solution to the Schrödinger equation on ${\mathbb{R}}^d$ with a power nonlinearity $\lambda |u{|}^{2\theta /d}u$ ($\lambda \in \mathbb{C}$, $0<\theta <1$) and the initial data…