This paper proposes a computer-assisted solution existence verification method for the stationary Navier-Stokes equation over general 3D domains. The proposed method verifies that the exact solution as the fixed point of the Newton iteration exists around the approximate solution through rigorous computation and error estimation. The explicit values of quantities required by applying the fixed point theorem are obtained by utilizing newly developed quantitative error estimation for finite element solutions to boundary value problems and eigenvalue problems of the Stokes equation.

翻译：本文为普通 3D 域的定点 Navier-Stokes 方程式提出了一个计算机辅助解决方案存在情况核查方法。拟议方法通过严格的计算和误差估计,核实作为牛顿迭代固定点的精确解决方案存在于近似解决方案周围。应用定点标值所需的明确数量值,通过使用新开发的量化误差估计,对边界值问题的定点元素解决方案和斯托克斯 方程式的二次值问题进行定量误差估计。