Strichartz estimates for Schrödinger equations with slowly decaying potentials

Abstract

For Schrödinger 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.

42 pages. Revised version to appear in JFA

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