标题： 斯特里哈茨估计及其在H型群上非线性薛定谔方程适定性中的应用 显示英文标题

标题： Strichartz estimates and its application to the well-posedness of the nonlinear Schrödinger equations on H-type groups

摘要： 本文的目的是给出在H型群上具有幂次非线性的非线性薛定谔方程的柯西问题的良好设定性结果。 为此，我们证明了色散估计和Strichartz估计。 尽管这些估计是由Hierro（2005）给出的，但其完整的证明无法找到。 我们修正了这些估计的陈述，给出了证明，并将其应用于非线性问题。 我们的良好设定性结果是对Bruno等人之前结果的改进。 显示英文摘要

摘要： The aim of this article is to give the well-posedness results for the Cauchy problem of the nonlinear Schr\"odinger equation with power type nonlinearities on H-type groups. To do this, we prove the dispersive estimate and Strichartz estimate. Although these estimates are given by Hierro (2005), its complete proofs cannot be find. We correct the statement of these estimates, give the proofs, and apply to the nonlinear problem. Our well-posedness results are an improvement of the previous result by Bruno et al.