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ENERGY CRITICAL NLS IN TWO SPACE DIMENSIONS
Journal article   Peer reviewed

ENERGY CRITICAL NLS IN TWO SPACE DIMENSIONS

J. Colliander, S. Ibrahim, M. Majdoub and N. Masmoudi
Journal of hyperbolic differential equations, Vol.6(3), pp.549-575
09/2009
DOI: https://doi.org/10.1142/S0219891609001927

Abstract

Mathematics Mathematics, Applied Physical Sciences Physics Physics, Mathematical Science & Technology
We investigate the initial value problem for a defocusing nonlinear Schrodinger equation with exponential nonlinearity i partial derivative(t)u + Delta u = u(e(4 pi|u|2) - 1) in R-t x R-x(2). 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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