Strichartz estimates for Schrodinger equations with slowly decaying potentials

摘要

For Schrodinger 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 vertical bar x vertical bar(-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. (C) 2020 Elsevier Inc. All rights reserved.