Mass Concentration Phenomena for the L2-Critical Nonlinear Schrödinger Equation

Bégout, Pascal and Vargas, Ana (2007) Mass Concentration Phenomena for the L2-Critical Nonlinear Schrödinger Equation. Transactions of the American Mathematical Society, vol. 359 (n° 11). pp. 5257-5282.

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Official URL: https://doi.org/10.1090/S0002-9947-07-04250-X

Abstract

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~\cite{MR99f:35184}, 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~\cite{MR1671214}. We also generalize to higher dimensions the results in Keraani~\cite{MR2216444} and Merle and Vega~\cite{MR1628235}.

Item Type: Article
Language: English
Date: 2007
Refereed: Yes
Uncontrolled Keywords: Schrödinger equations, restriction theorems, Strichartz's estimate, blow-up
Keywords (French): équations de Schrödinger, théorèmes de restriction, estimations de Strichartz, explosion
Subjects: G- MATHEMATIQUES
Divisions: Institut de mathématiques de Toulouse, TSE-R (Toulouse)
Site: UT1
Date Deposited: 08 Mar 2018 14:04
Last Modified: 08 Mar 2018 14:04
URI: http://publications.ut-capitole.fr/id/eprint/25109

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