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

Zhang Xiaoyi

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arXiv · math/0411423

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

Zhang Xiaoyi

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Abstract

In this paper,we show that spherical bounded energy solution of the defocusing 3D energy critical Schrödinger equation with harmonic potential, $(i\partial_t + \frac Δ2+\frac {|x|^2}2)u=|u|^4u$, exits globally and scatters to free solution in the space $Σ=H^1\bigcap\mathcal F H^1$. We preclude the concentration of energy in finite time by combining the energy decay estimates.

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Zhang Xiaoyi. 2004-11-19. Global wellposedness and scattering for 3D Schrödinger equations with harmonic potential and radial data. https://arxiv.org/abs/math/0411423

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