Global existence for semilinear Schrödinger equations in 2+1 dimensions

This paper is concerned with global well-posedness of the 2-dimensional defocusing semilinear Schrödinger equation iut+Δu=|u|2mu in the Sobolev space Hs(R2). In a previous work of Guo and Cui [C. Guo, S. Cui, Global existence for 2D nonlinear Schrödinger equations via high-low frequency decomposition method, J. Math. Anal. Appl. 324 (2006) 882–907] it was proved that global well-posedness holds in Hs(R2) for . That result is obtained by using the high-low frequency decomposition method. In this paper we apply the I-method to improve that result, and prove that global well-posedness holds in Hs(R2) for .