Strichartz estimates for Schrödinger equations with slowly decaying potentials
Strichartz estimates for Schrödinger equations with slowly decaying potentials
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DOI：
10.1016/j.jfa.2020.108789
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发表时间：
2018-08
影响因子：
1.7
通讯作者：
H. Mizutani
中科院分区：
文献类型：
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作者：
H. Mizutani
对于具有一类慢衰减排斥势的薛定谔方程，我们证明了其解满足任意容许对的全局时间Strichartz估计。我们所允许的位势包括具有Z>；0和0<；μ<；2的三维和更高维正齐次位势Z|x|Lt；，特别是排斥库仑势。该证明使用了散射理论中的几种技巧，如Isozaki-Kitada类型的长时间参数线构造、传播估计和局部衰减估计。
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.