Differential and Integral Equations

Scattering for the critical 2-D NLS with exponential growth

Hajer Bahouri, Slim Ibrahim, and Galina Perelman

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Abstract

In this article, we establish in the radial framework the $H^1$-scattering for the critical 2-D nonlinear Schrödinger equation with exponential growth. Our strategy relies on both the a priori estimate derived in [10, 23] and the characterization of the lack of compactness of the Sobolev embedding of $H_{rad}^1(\mathbb R^2)$ into the critical Orlicz space ${\mathcal L}(\mathbb R^2)$ settled in [4]. The radial setting, and particularly the fact that we deal with bounded functions far away from the origin, occurs in a crucial way in our approach.

Article information

Source
Differential Integral Equations, Volume 27, Number 3/4 (2014), 233-268.

Dates
First available in Project Euclid: 30 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.die/1391091365

Mathematical Reviews number (MathSciNet)
MR3161603

Zentralblatt MATH identifier
1324.35167

Subjects
Primary: 35Q55 35B33: Critical exponents 35B40: Asymptotic behavior of solutions 35P25: Scattering theory [See also 47A40]

Citation

Bahouri, Hajer; Ibrahim, Slim; Perelman, Galina. Scattering for the critical 2-D NLS with exponential growth. Differential Integral Equations 27 (2014), no. 3/4, 233--268. https://projecteuclid.org/euclid.die/1391091365


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