不可压Navier-Stokes方程无粘极限的研究

不可压Navier-Stokes方程的粘性消失极限问题研究当粘性系数趋向0时，系统方程解的收敛过程，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。尤其是在有物理边界的情况下，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。一直以来，都是流体力学数学研究领域的核心内容，受到广泛关注，近期的研究取得了重要的进展。 本项目主要对Navier-Stokes方程和依赖密度的Navier-Stokes方程等不可压系统在Slip及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。通过对相应边界条件的边界层进行深入的分析，就依赖密度的Navier-Stokes方程，以期获得在Slip边界条件下的原创性收敛结果；就Navier-Stokes方程，以期获得分别在Slip和No-slip边界条件下较以往更为深刻的收敛结果。

The inviscid limit problem for incompressible Navier-Stokes systems which study the convergence prosses of the solutions of the systems. It 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 layer. In this grant, we will investigate the inviscid limit problem for the Navier-Stokes systems and density-dependent Navier-Stokes systems in bounded domains with Slip or No-slip boundary conditions, and the associated bounded layer problems. For the density-dependent Navier-Stokes systems, we will look for some first convergence results under slip boundary conditions. For the Navier-Stokes systems, We will look for some further convergence results both under slip and no-slip boundary conditions.