1204.0130 (Wei Dai)

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

Wei Dai

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 $4View original: http://arxiv.org/abs/1204.0130