Differential and Integral Equations
- Differential Integral Equations
- Volume 24, Number 9/10 (2011), 923-940.
A new proof of long-range scattering for critical nonlinear Schrödinger equations
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.
Differential Integral Equations, Volume 24, Number 9/10 (2011), 923-940.
First available in Project Euclid: 20 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
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