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arXiv · 1901.00957

Dispersive estimates for time and space fractional Schrödinger equations

Xiaoyan Su·Shiliang Zhao·Miao Li
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Abstract

In this paper, we consider the Cauchy problem for the fractional Schrödinger equation $i D_t^αu + (-Δ)^{\fracβ{2}} u =0$ with $0<α<1$, $β>0$. We establish the dispersive estimates for the solutions. In particular, we prove that the decay rates are sharp.

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Xiaoyan Su, Shiliang Zhao, Miao Li. 2019-01-04. Dispersive estimates for time and space fractional Schrödinger equations. https://arxiv.org/abs/1901.00957

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