In the talk we shall present some recent results obtained with F. Merle about compactness of blow up solutions of the critical nonlinear Schrödinger equation for initial data in ${L}^{2}\left({\mathbf{R}}^{2}\right)$. 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.

@article{JEDP_1998____A13_0, author = {Gonzalez, Luis Vega}, title = {Remarks on global existence and compactness for $L^2$ solutions in the critical nonlinear schr\"odinger equation in 2D}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, publisher = {Universit\'e de Nantes}, year = {1998}, zbl = {01808722}, language = {en}, url = {http://www.numdam.org/item/JEDP_1998____A13_0} }

Gonzalez, Luis Vega. Remarks on global existence and compactness for $L^2$ solutions in the critical nonlinear schrödinger equation in 2D. Journées équations aux dérivées partielles (1998), article no. 13, 9 p. http://www.numdam.org/item/JEDP_1998____A13_0/

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