# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 37 (2008) pp.861-870

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### Abstract

The initial value problem for the defocusing cubic nonlinear Schrödinger equation on ${\Bbb R}^2$ is locally well-posed in Hs for s ≥ 0. The L^2-space norm is invariant under rescaling to the equation, then the critical regularity is s = 0. In this note, we prove the global well-posedness in Hs for all s > 1/2. The proof uses the almost conservation approach by adding additional (non-resonant) correction terms to the original almost conserved energy.

MSC(Primary) 35Q55 Strichartz estimate, nonlinear Schrödinger equation, global well-posedness.