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|−μ with Z>0 and 0<μ<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.