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arXiv · 1207.2028

Mass Concentration Phenomena for the L^2-Critical Nonlinear Schr{\"o}dinger Equation

Pascal Bégout·Ana Vargas
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Abstract

In this paper, we show that any solution of the nonlinear Schr{{\"o}}dinger 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}.

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Pascal Bégout, Ana Vargas. 2012-07-09. Mass Concentration Phenomena for the L^2-Critical Nonlinear Schr{\"o}dinger Equation. https://doi.org/10.1090/s0002-9947-07-04250-x

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