Global well-posedness for the defocusing, quintic nonlinear Schrödinger equation in one dimension

2009/10/20 by Dodson, Benjamin
#35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0910.3964

Abstract

In this paper, we prove global well-posedness for low regularity data for the one dimensional quintic defocusing nonlinear Schrödinger equation. We show that a unique solution exists for u₀ ∈ H^s(R), s > 8/29. This improves the result in [13], which proved global well-posedness for s > 1/3. The main new argument is that we obtain almost Morawetz estimates with improved error.

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