Strichartz estimates for Schr\"odinger equations with slowly decaying potentials

Haruya Mizutani

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arXiv · 1808.06987

Strichartz estimates for Schr\"odinger equations with slowly decaying potentials

Haruya Mizutani

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Abstract

For Schr\"odinger equations with a class of slowly decaying repulsive potentials, we show that the solution satisfies global-in-time Strichartz estimates for any admissible pairs. Our admissible class of potentials includes the positive homogeneous potential $Z|x|^{-\mu}$ with $Z>0$ and $0<\mu<2$ in three and higher dimensions, especially the repulsive Coulomb potential. The proof employs several techniques from scattering theory such as the long time parametrix construction of Isozaki-Kitada type, propagation estimates and local decay estimates.

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Haruya Mizutani. 2018-08-21. Strichartz estimates for Schr\"odinger equations with slowly decaying potentials. https://arxiv.org/abs/1808.06987

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