In this article, we establish scale-invariant Strichartz estimates for the Schrödinger equation on arbitrary compact globally symmetric spaces and some bilinear Strichartz estimates on products of rank-one spaces. As applications, we provide local well-posedness results for nonlinear Schrödinger equations on such spaces in both subcritical and critical regularities.

中文翻译：

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紧致全局对称空间上的Schrödinger方程

在本文中，我们在任意紧致的全局对称空间上为Schrödinger方程建立了尺度不变的Strichartz估计，并在秩为1的乘积上建立了一些双线性Strichartz估计。作为应用程序，我们为处于次临界和临界规律性的此类空间上的非线性Schrödinger方程提供局部适定性结果。