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arXiv · 1502.02212

Decay and scattering of solutions to nonlinear Schr\"odinger equations with regular potentials for nonlinearities of sharp growth

Ze Li·Lifeng Zhao
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Abstract

In this paper, we prove the decay and scattering in the energy space for nonlinear Schr\"odinger equations with regular potentials in $\Bbb R^d$ namely, $i{\partial _t}u + \Delta u - V(x)u + \lambda |u|^{p - 1}u = 0$. We will prove decay estimate and scattering of the solution in the small data case when $1+\frac{2}{d}<p\le1+\frac{4}{d-2}$, $d\ge3$. The index $1+\frac{2}{d}$ is sharp for scattering concerning the result of W. Strauss [21].

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Ze Li, Lifeng Zhao. 2015-02-08. Decay and scattering of solutions to nonlinear Schr\"odinger equations with regular potentials for nonlinearities of sharp growth. https://arxiv.org/abs/1502.02212

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