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：本文在最小正则性假设下，分析了Lipschitz域上定常Navier-Stokes方程的Nitsche方法。该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体系。基于标准小数据假设，利用Banach–Nečas–Babuška定理与Banach不动点定理，我们证明了离散问题的适定性，并给出了近似误差的最优收敛阶。此外，我们提出了一种VMS-LES稳定化格式，可用于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，验证了理论结果的有效性。