Remarks on global existence and compactness for L 2 solutions in the critical nonlinear schrödinger equation in 2D

In the talk we shall present some recent results obtained with F. Merle about compactness of blow up solutions of the critical nonlinear Schrodinger equation for inital data in L^R). They are based on and are complementary to some previous work of J. Bourgain about the concentration of the solution when it approaches to the blow up time.