Differential and Integral Equations

A new proof of long-range scattering for critical nonlinear Schrödinger equations

Jun Kato and Fabio Pusateri

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Abstract

We present a new proof of global existence and long range scattering, from small initial data, for the one--dimensional cubic gauge invariant nonlinear Schrödinger equation, and for Hartree equations in dimension $n \geq 2$. The proof relies on an analysis in Fourier space, related to the recent works of Germain, Masmoudi, and Shatah on space-time resonances. An interesting feature of our approach is that we are able to identify the long range phase correction term through a very natural stationary phase argument.

Article information

Source
Differential Integral Equations, Volume 24, Number 9/10 (2011), 923-940.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012893

Mathematical Reviews number (MathSciNet)
MR2850346

Zentralblatt MATH identifier
1249.35307

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Citation

Kato, Jun; Pusateri, Fabio. A new proof of long-range scattering for critical nonlinear Schrödinger equations. Differential Integral Equations 24 (2011), no. 9/10, 923--940. https://projecteuclid.org/euclid.die/1356012893


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