Mass concentration phenomena for the L2-critical nonlinear Schrdinger equation

In this paper, we show that any solution of the nonlinear Schrödinger equation iut + ∆u ± |u | 4N u = 0, which blows up in finite time, satisfies a mass concentration phenomena near the blow-up time. Our proof is essentially based on the Bourgain’s one [3], which has established this result in the bidimensional spatial case, and on a generalization of Strichartz’s inequality, where the bidimensional spatial case was proved by Moyua, Vargas and Vega [17]. We also generalize to higher dimensions the results in Keraani [13] and Merle and Vega [15]. 1 Introduction and main results Let γ ∈ R \ {0} and let 0 6 α 6 4N. It is well-known that for any u0 ∈ L2(RN), there exists a unique maximal solutio