CPAA
Improved almost Morawetz estimates for the cubic nonlinear Schrödinger equation
Benjamin Dodson
Communications on Pure & Applied Analysis 2011, 10(1): 127-140 doi: 10.3934/cpaa.2011.10.127
We prove global well-posedness for the cubic, defocusing, nonlinear Schrödinger equation on $R^2$ with data $u_0 \in H^s(R^2)$, $s > 1/4$. We accomplish this by improving the almost Morawetz estimates in [9].
keywords: Partial di erential equations harmonic analysis.
DCDS
Global well-posedness and scattering for the defocusing, cubic nonlinear Schrödinger equation when $n = 3$ via a linear-nonlinear decomposition
Benjamin Dodson
Discrete & Continuous Dynamical Systems - A 2013, 33(5): 1905-1926 doi: 10.3934/dcds.2013.33.1905
In this paper, we prove global well-posedness and scattering for the defocusing, cubic nonlinear Schrödinger equation when $n = 3$ and $u_{0} \in H^{s}(\mathbf{R}^{3})$, $s > 5/7$. To this end, we utilize a linear-nonlinear decomposition, similar to the decomposition used in [20] for the wave equation.
keywords: Nonlinear Schrödinger equation.

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