Global well-posedness and scattering for the defocusing, \(L^2\)-critical nonlinear Schrödinger equation when \(d \geq 3\)

DOI10.1090/S0894-0347-2011-00727-3zbMATH Open1236.35163arXiv1010.0040OpenAlexW1650157153MaRDI QIDQ2879889

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Publication date: 5 April 2012

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Abstract: In this paper we prove that the defocusing, quintic nonlinear Schr"odinger initial value problem is globally well-posed and scattering for $u_{0}in{L}^2(mathbfR)$. To do this, we will prove a frequency localized interaction Morawetz estimate similar to the estimate made in [11]. Since we are considering an $L^2$ - critical initial value problem we will localize to low frequencies.

Full work available at URL: https://arxiv.org/abs/1010.0040

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