%0 Journal Article
%@ 0002-9947
%A Bégout, Pascal
%A Vargas, Ana
%D 2007
%F publications:35020
%I MacMillan Company
%J Transactions of the American Mathematical Society (TRAN)
%K Schrödinger equation
%K restriction theorems
%K Strichartz's estimate
%K blow-up
%N 11
%P 5257-5282
%T Mass Concentration Phenomena for the L^2-Critical Nonlinear Schrödinger Equation
%U https://publications.ut-capitole.fr/id/eprint/35020/
%V 359
%X In this paper, we show that any solution of the nonlinear Schrödinger equation $iu_t+\Delta u\pm|u|^\frac{4}{N}u=0,$ 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].