Mass concentration phenomena for the -critical nonlinear Schrödinger equation |
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Authors: | Pascal Bé gout Ana Vargas |
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Affiliation: | Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Bo{î}te Courrier 187, 4, place Jussieu, 75252 Paris Cedex 05, France ; Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid 28049 Madrid, Spain |
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Abstract: | In this paper, we show that any solution of the nonlinear Schrödinger equation which blows up in finite time, satisfies a mass concentration phenomena near the blow-up time. Our proof is essentially based on Bourgain's (1998), 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 (1999). We also generalize to higher dimensions the results in Keraani (2006) and Merle and Vega (1998). |
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Keywords: | Schr" {o}dinger equations, restriction theorems, Strichartz's estimate, blow-up |
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