The energy-critical quantum harmonic oscillator
The energy-critical quantum harmonic oscillator
We consider the energy critical nonlinear Schrödinger equation in dimensions 3 and above with a harmonic oscillator potential. In the defocusing situation, we prove global wellposedness for all initial data in the energy space Σ. This extends a result of Killip-Visan-Zhang, who treated the radial case. For the focusing nonlinearity, …