Lifespan of solutions for the nonlinear Schrödinger equation without gauge invariance
arXiv:1211.6928
Abstract
We study the lifespan of solutions for the nonlinear Schrödinger equation id_{t}u+Δu=λ|u|^{p}, (t,x)\in[0,T)\timesR^{n}, with the initial condition, where 1<p\leq 1+2/n and λ\in C. Our main aim in this paper is to prove an upper bound of the lifespan in the subcritical case 1<p<1+2/n.
10pages