We establish Strichartz estimates for the regularized Schrödinger equation on a two dimensional compact Riemannian manifold without boundary. As a consequence we deduce global existence and uniqueness results for the Cauchy problem for the nonlinear regularized Schrödinger equation and we prove under the geometric control condition the Kato smoothing effect for solutions of this equation in this particular geometries.

中文翻译：

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紧流形上非线性正则Schrödinger方程的Kato平滑效应。

我们在二维无边界黎曼流形上建立正则化Schrödinger方程的Strichartz估计。结果，我们推导了非线性正则化Schrödinger方程的Cauchy问题的全局存在性和唯一性结果，并证明了在几何控制条件下，该方程在该特定几何形状中的解的Kato平滑效果。