On 2D Nonlinear Schrödinger Equations with Data on R×T

✍ Scribed by H Takaoka; N Tzvetkov

• Book ID: 102587635
• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 142 KB
• Volume: 182
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.2000.3732

✦ Synopsis

We prove L 2 global well-posedness results for 2D (subcritical and critical) nonlinear Schro dinger equations with data on R_T. We use methods of the periodic case due to J. Bourgain. The main ingredient in the proof is the L 4 &L 2 Strichartz inequality for the free evolution which fails in the purely periodic setting.

2001 Academic Press

When the problem is posed on R_R we have the following global well-posedness result.

Theorem 1 ([5, 7, 15, 16, 20]). Let 1<p<3. Then the Cauchy problem (1) (2) is globally well-posed for any data in L 2 (R_R). In the critical case