In this paper we prove the orthonormal Strichartz estimates for the higher order and fractional Schrödinger, wave, Klein-Gordon and Dirac equations with potentials. As in the case of the Schrödinger operator, the proofs are based on the smooth perturbation theory by T. Kato. However, for the Klein-Gordon and Dirac equations, we also use a method of the microlocal analysis in order to prove the estimates for wider range of admissible pairs. As applications we prove the global existence of a solution to the higher order or fractional Hartree equation with potentials which describes the dynamics of infinitely many particles. We also give a local existence result for the semi-relativistic Hartree equation with electromagnetic potentials. As another application, the refined Strichartz estimates are proved for higher order and fractional Schrödinger, wave and Klein-Gordon equations.

中文翻译：

---

具有势的色散方程的正交 Strichartz 估计

在本文中，我们证明了具有势的高阶分数阶薛定谔方程、波方程、克莱因-戈登方程和狄拉克方程的正交 Strichartz 估计。与薛定谔算子的情况一样，证明基于 T. Kato 的平滑微扰理论。然而，对于 Klein-Gordon 和 Dirac 方程，我们还使用微局域分析的方法来证明更广泛的可接受对的估计。作为应用，我们证明了具有描述无限多个粒子动力学的势的高阶或分数哈特里方程解的全局存在性。我们还给出了具有电磁势的半相对论 Hartree 方程的局部存在性结果。作为另一个应用，改进的 Strichartz 估计被证明适用于高阶和分数阶薛定谔方程、波方程和克莱因-戈登方程。