Global Well-posedness and Scattering for the Focusing Nonlinear Schrödinger Equation in the Nonradial Case
نویسنده
چکیده
The energy-critical, focusing nonlinear Schrödinger equation in the nonradial case reads as follows: i∂tu = −∆u− |u| 4 N−2 u, u(x, 0) = u0 ∈ H(R ), N ≥ 3. Under a suitable assumption on the maximal strong solution, using a compactness argument and a virial identity, we establish the global well-posedness and scattering in the nonradial case, which gives a positive answer to one open problem proposed by Kenig and Merle [Invent. Math. 166 (2006), 645–675].
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