标题： 高阶薛定谔方程的Strichartz估计与部分正则初始数据 显示英文标题

标题： Strichartz estimates for higher order Schrödinger equations with Partial regular initial data

摘要： 在本文中，我们为具有部分正则性初始数据的高阶薛定谔方程建立了改进的Strichartz估计。所谓部分正则性，指的是初始数据不需要具有完整的Sobolev正则性，而只需相对于一部分空间变量具有正则性。作为这些估计的应用，我们研究了具有幂型非线性的非线性薛定谔方程的适定性。此外，我们将分析扩展到在部分正则性下定义的Dunkl薛定谔方程，该方程相对于两个不同的根系进行定义。这种扩展带来了重大挑战，主要是由于在Dunkl环境下缺乏合适的平稳相位方法。为了克服这一困难，我们开发了一个新结果，该结果提供了将平稳相位方法适应到Dunkl分析框架中的方法。 显示英文摘要

摘要： In this paper, we establish refined Strichartz estimates for higher-order Schr\"odinger equations with initial data exhibiting partial regularity. By partial regularity, we mean that the initial data are not required to have full Sobolev regularity but only regularity with respect to a subset of the spatial variables. As an application of these estimates, we investigate the well-posedness of nonlinear Schr\"odinger equations with power-type nonlinearities. In addition, we extend our analysis to the Dunkl Schr\"odinger equations under partial regularity, defined with respect to two distinct root systems. This extension poses significant challenges, mainly due to the lack of a suitable stationary phase method in the Dunkl setting. To overcome this difficulty, we develop a new result that provides an adaptation of the stationary phase method to the framework of Dunkl analysis.