Arbitrary growth and oscillation versus finite time blow up in nonlinear Schrödinger equations

Gonçalves Ribeiro, J.M.

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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 $L^{2} (𝐑^{2})$ . 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.