Abstract
We show that the blow up solution with data in energy spaces H1 of the nonlinear Schrödinger equation i ut + Δu + |u|αu = 0 has a concentration behavior in the critical Sobolev space Ḣsα (0 < sα = n/2 - 2/α ≤ 1) if the time variable tends to the blow up time. Moreover, the blow up points in ℝn are also quantified in the L2 critical case α = 4/n.
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