Continuous dependence for $H^{2}$ critical nonlinear Schrödinger equations in high dimensions

Details Continuous dependence for $H^{2}$ critical nonlinear Schrödinger equations in high dimensions Continuous dependence for $H^{2}$ critical nonlinear Schrödinger equations in high dimensions

2012-03-31

arxiv.org/abs/1204.0130v1

Mathematics

Analysis of PDEs

12 pages, no figure

Scientific paper

The global existence of solutions in $H^{2}$ is well known for $H^{2}$ critical nonlinear Schr\"{o}dinger equations with small initial data in high dimensions $d\geq8$. However, even though the solution is constructed by a fixed-point technique, continuous dependence in $H^{2}$ does not follow from the contraction mapping argument. Comparing with the low dimension cases $4

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