On the blow up time estimation to the Schrödinger equation

Abstract

There is considered the Schrödinger equation ∂u/∂t= i Δu+ i|u|^p , u, t > 0, with initial condition u(0, x)= u₀(x),  x ∈ Rⁿ, n = 1. We prove the existence of the u₀(x) such, that the blow up time estimation increases if p increases in the intervale 4 < p < p₀.