The mass-critical fourth-order Schrodinger equation in high dimensions

2009/06/08 by Pausader, Benoit, Shao, Shuanglin
#35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0906.1547

Abstract

We prove global wellposedness and scattering for the Mass-critical homogeneous fourth-order Schrodinger equation in high dimensions n>4, for general L² initial data in the defocusing case, and for general initial data with Mass less than certain fraction of the Mass of the Ground State in the focusing case.

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• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
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• Global well-posedness and scattering for the higher-dimensional energy-critical non-linear Schrodinger equation for radial data