不可压流体力学系统的粘性消失极限问题是流体力学系统研究的经典数学问题。对理解流体的湍流运动和边界层现象有着重要的物理背景和浓厚的数学研究兴趣。尤其是当有物理边界时，由于边界层的出现，数学研究的难度更大，是极具挑战性的问题,很长一段时间曾鲜有结果。近期的工作取得了重要的进展，这为今后的研究提供了宝贵的机遇。. 本项目主要对Navier-Stokes方程和非齐次不可压Navier-Stokes方程等不可压系统在Slip或No-slip边界条件下的粘性消失极限等重要问题展开进一步深入地研究。就Navier-Stokes方程在Slip和No-slip边界条件下获得较以往更为深刻的结果；通过对相应边界条件的相容性及边界层进行深入的分析，就非齐次不可压Navier-Stokes方程在Slip边界条件下获得原创性的收敛性结果。

The vanishing viscosity limit problem of the incompressible Navier-Stokes systems is a classical issue in the mathematical study of the fluid dynamical systems, and has important physical applications and mathematical interests. In the presence of physical boundary,the situation is much more complicated, and the problem become challenging due to the boundary layers, and few result has known for a long time. Recently, some important works have been done to these problems. It then gives out great opportunityies to do further studies.. In this grant, we will investigate the vanishing viscosity limit problem for the Navier-Stokes systems and the non-homogeneous Navier-Stokes systems in bounded domains with Slip or No-slip boundary conditions, and the associated bounded layer problems. For the Navier-Stokes systems, we will look for some further convergence results with slip or no-slip boundary conditions. For the non-homogeneous Navier-Stokes systems, we will look for the uniform regularity and the related convergence results under slip boundary conditions.