Geodesic
The cubic nonlinear Schrödinger equation in two dimensions with radial data
Journal of the European Mathematical Society, Tome 11 (2009) no. 6, pp. 1203-1258 Cet article a éte moissonné depuis la source EMS Press

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We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation iut​+Δu=±∣u∣2u for large spherically symmetric Lx2​(R2) initial data; in the focusing case we require, of course, that the mass is strictly less than that of the ground state. As a consequence, we deduce that in the focusing case, any spherically symmetric blowup solution must concentrate at least the mass of the ground state at the blowup time.
DOI : 10.4171/jems/180
Classification : 35-XX, 00-XX
Keywords: Nonlinear Schrödinger equation, scattering, mass-critical, virial identity 
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     author = {Rowan Killip and Terence Tao and Monica Vișan},
     title = {The cubic nonlinear {Schr\"odinger} equation in two dimensions with radial data},
     journal = {Journal of the European Mathematical Society},
     pages = {1203--1258},
     year = {2009},
     volume = {11},
     number = {6},
     doi = {10.4171/jems/180},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/180/}
}
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Rowan Killip; Terence Tao; Monica Vișan. The cubic nonlinear Schrödinger equation in two dimensions with radial data. Journal of the European Mathematical Society, Tome 11 (2009) no. 6, pp. 1203-1258. doi: 10.4171/jems/180

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