Energy Critical NLS in two space dimensions

Details Energy Critical NLS in two space dimensions Energy Critical NLS in two space dimensions

2008-06-18

arxiv.org/abs/0806.2979v1

Mathematics

Analysis of PDEs

27 pages, submitted

Scientific paper

We investigate the initial value problem for a defocusing nonlinear
Schr\"odingerequation with exponential nonlinearity. We identify subcritical,
critical and supercritical regimes in the energy space. We establish global
well-posedness in the subcritical and critical regimes. Well-posedness fails to
hold in the supercritical case.

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