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

We prove L2 global well-posedness results for 2D (subcritical and critical) nonlinear Schrödinger 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 L4−L2 Strichartz inequality for the free evolution which fails in the purely periodic setting.