Remarks on the blowup for the L2-critical nonlinear Schrödinger equations

Taoufik Hmidi; Sahbi Keraani

doi:10.1137/050624054

Remarks on the blowup for the L²-critical nonlinear Schrödinger equations

Taoufik Hmidi, Sahbi Keraani

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

This paper is dedicated to the formation of singularities of the solutions of L²-entical nonlinear Schrödinger equations. We prove a refined compactness lemma adapted to the blowup analysis, and we use it to improve the recent result by Colliander et al. [Math. Res. Lett., 12 (2005), pp. 357-375] on the concentration in the L²-critical nonlinear Schrödinger equation below H¹.

Original language	English (US)
Pages (from-to)	1035-1047
Number of pages	13
Journal	SIAM Journal on Mathematical Analysis
Volume	38
Issue number	4
DOIs	https://doi.org/10.1137/050624054
State	Published - 2006

Keywords

Blowup
Mass concentration
Time dependent Schrödinger equation

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

Access to Document

10.1137/050624054

Cite this

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abstract = "This paper is dedicated to the formation of singularities of the solutions of L2-entical nonlinear Schr{\"o}dinger equations. We prove a refined compactness lemma adapted to the blowup analysis, and we use it to improve the recent result by Colliander et al. [Math. Res. Lett., 12 (2005), pp. 357-375] on the concentration in the L2-critical nonlinear Schr{\"o}dinger equation below H1.",

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KW - Time dependent Schrödinger equation

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