Global wellposedness and scattering for 3D Schrödinger equations with harmonic potential and radial data

Details Global wellposedness and scattering for 3D Schrödinger equations with harmonic potential and radial data Global wellposedness and scattering for 3D Schrödinger equations with harmonic potential and radial data

2004-11-19

arxiv.org/abs/math/0411423v1

Mathematics

Analysis of PDEs

39 pages

Scientific paper

In this paper,we show that spherical bounded energy solution of the defocusing 3D energy critical Schr\"odinger equation with harmonic potential, $(i\partial_t + \frac {\Delta}2+\frac {|x|^2}2)u=|u|^4u$, exits globally and scatters to free solution in the space $\Sigma=H^1\bigcap\mathcal F H^1$. We preclude the concentration of energy in finite time by combining the energy decay estimates.

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