In this paper, we analyze the Nitsche's method for the stationary Navier-Stokes equations on Lipschitz domains under minimal regularity assumptions. Our analysis provides a robust formulation for implementing slip (i.e. Navier) boundary conditions in arbitrarily complex boundaries. The well-posedness of the discrete problem is established using the Banach Ne\v{c}as Babu\v{s}ka and the Banach fixed point theorems under standard small data assumptions, and we also provide optimal convergence rates for the approximation error. Furthermore, we propose a VMS-LES stabilized formulation, which allows the simulation of incompressible fluids at high Reynolds numbers. We validate our theory through numerous numerical tests in well established benchmark problems.

翻译：本文在Lipschitz区域上，于最小正则性假设下分析了定常Navier-Stokes方程的Nitsche方法。我们的分析为在任意复杂边界上实现滑移（即Navier）边界条件提供了稳健的公式。在标准小数据假设下，利用Banach-Nečas-Babuška定理和Banach不动点定理建立了离散问题的适定性，并给出了逼近误差的最优收敛速度。此外，我们提出了一种VMS-LES稳定化格式，使得能够模拟高雷诺数下的不可压缩流体。通过多个经典基准问题的数值实验验证了我们的理论。