Analysis of nonlinear partial differential equations with nonlocal property

在这个项目中，我们考虑具有非局部性质的非线性偏微分方程。我们得到了不可压缩Navier-Stokes流的正则性和渐近性，以及某些分数阶扩散方程基本解的性质。此外，我们还介绍了非局部偏微分方程的一些分析方法。我们期望这些方法可以应用于未来的研究。

In this project, we considered nonlinear partial differential equations with nonlocal property. We obtained some results on the regularity and the asymptotic behavior of the incompressible Navier-Stokes flows and the property of the fundamental solutions for certain fractional diffusion equations. Besides these results, we introduced some methods for the analysis of the nonlocal partial differential equations. We expect these methods can be applied for future research.