Scattering for the critical 2-D NLS with exponential growth. (English) Zbl 1324.35167

Bahouri, Hajer; Ibrahim, Slim; Perelman, Galina

Differ. Integral Equ. 27, No. 3-4, 233-268 (2014).

The title of the article is already quite descriptive. The authors consider the Cauchy problem for radial initial data. This allows them to utilize sharp Moser-Trudinger type inequalities with best Sobolev constant. To compensate for the lack of compactness at infinity, they utilize a virial type identity that they establish in Section 3.1. This is a compactly written paper with a clear result.

Reviewer: Alp Eden (Istanbul)

MSC:

35Q55	NLS equations (nonlinear Schrödinger equations)
35B33	Critical exponents in context of PDEs
35B40	Asymptotic behavior of solutions to PDEs
35P25	Scattering theory for PDEs

Keywords:

nonlinear Schrödinger equation; Cauchy problem; scattering; Moser-Trudinger inequalities