Resonant decompositions and the I-method for cubic nonlinear Schrodinger on R^2 - Mathematics Analysis of PDEsReport as inadecuate




Resonant decompositions and the I-method for cubic nonlinear Schrodinger on R^2 - Mathematics Analysis of PDEs - Download this document for free, or read online. Document in PDF available to download.

Abstract: The initial value problem for the cubic defocusing nonlinear Schr\-odingerequation $i \partial t u + \Delta u = |u|^2 u$ on the plane is shown to beglobally well-posed for initial data in $H^s \R^2$ provided $s>1-2$. Theproof relies upon an almost conserved quantity constructed using multilinearcorrection terms. The main new difficulty is to control the contribution ofresonant interactions to these correction terms. The resonant interactions aresignificant due to the multidimensional setting of the problem and someorthogonality issues which arise.



Author: J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao

Source: https://arxiv.org/







Related documents