Improved almost Morawetz estimates for the cubic nonlinear Schrödinger equation

Benjamin Dodson

doi:10.3934/cpaa.2011.10.127

Article Contents

2011, Volume 10, Issue 1: 127-140. Doi: 10.3934/cpaa.2011.10.127

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Improved almost Morawetz estimates for the cubic nonlinear Schrödinger equation

Benjamin Dodson^1,

1.
Department of Mathematics, University of California - Berkeley, 970 Evans Hall, Number 3840; Berkeley, CA 94720-3840

Received: January 2010

Revised: March 2010

Published: January 2011

Abstract / Introduction Related Papers Cited by

Abstract

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 dierential equations,
harmonic analysis.

Mathematics Subject Classification: Primary: 35Q55.

Citation:

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References

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