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

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 $u_0\in H^s(\mathbf{R})$, $s>8/29$. 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.

25 pages

References in corpus (4)

• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
• Improved interaction Morawetz inequalities for the cubic nonlinear Schrödinger equation on ${\mathbb{R}}^2$
• Improved almost Morawetz estimates for the cubic nonlinear Schrodinger equation