Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case
作者： J. Bourgain
DOI: 10.1090/S0894-0347-99-00283-0
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摘要: is globally wellposed in time. More precisely, we obtain a unique solution u = uφ ∈ CH1([0,∞[) such that for all time, u(t) depends continuously on the data φ (in fact, dependence even real analytic here). Moreover, there scattering t→∞. The same statement holds radial H, s ≥ 1 and proves particular global existence of classical solutions radially symmetric case. Also this issue was open. Thus analogue NLS result wave equation with quintic nonlinearity obtained by M. Struwe [Str] case (and Grillakis [Gr], [S-S], general). In equation, proof based following two different facts:
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