On the blow up phenomenon for the L critical nonlinear Schrödinger Equation
نویسنده
چکیده
with u0 ∈ H1 = {u,∇u ∈ L2(RN )} in dimension N ≥ 1. This equation for N = 2 appears in physics as a universal model to describe self trapping of waves propagating in nonlinear media. The physical expectation for large smooth data is the concentration of part of the L2 mass in finite time corresponding to the focusing of the laser beam. If some explicit examples of this phenomenon are known, and despite a number of both numerical and mathematical works, a general description of blow up dynamics is mostly open.
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