Global well-posedness and scattering for the defocusing,\n L²-critical, nonlinear Schr "odinger equation when d = 1

2010/09/30 by Benjamin Dodson, Dodson, Benjamin · 4 citations
Mathematics · #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.1010.0040

Abstract

In this paper we prove that the defocusing, quintic nonlinear Schr "odinger\ninitial value problem is globally well-posed and scattering for u₀ \∈\nL²(\R). To do this, we will prove a frequency localized interaction\nMorawetz estimate similar to the estimate made in [11]. Since we are\nconsidering an L² - critical initial value problem we will localize to low\nfrequencies.\n

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