SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2945-2968, January 2020.
In a plane polygon $P$ with straight sides, we prove analytic regularity of the Leray--Hopf solution of the stationary, viscous, and incompressible Navier--Stokes equations. We assume small data, analytic volume force, and no-slip boundary conditions. Analytic regularity is quantified in so-called countably normed, corner-weighted spaces with homogeneous norms. Implications of this analytic regularity include exponential smallness of Kolmogorov $N$-widths of solutions, exponential convergence rates of mixed $hp$-discontinuous Galerkin finite element and spectral element discretizations, and model order reduction techniques.

中文翻译：

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多边形中不可压缩的Navier-Stokes方程的解析正则性

SIAM数学分析期刊，第52卷，第3期，第2945-2968页，2020
年1月。在具有直边的平面多边形$ P $中，我们证明了固定，粘性和不可压缩的Leray-Hopf解的解析正则性Navier-Stokes方程。我们假设数据较小，分析体积力和无滑移边界条件。解析规律性在具有均等范数的所谓可数范数，角加权空间中进行量化。这种分析规律性的含义包括解的Kolmogorov $ N $宽度的指数小，混合的$ hp $不连续的Galerkin有限元和谱元离散化的指数收敛速度以及模型阶数减少技术。