论文标题
多边形中不可压缩的Navier-Stokes方程的分析规律性
Analytic regularity for the incompressible Navier-Stokes equations in polygons
论文作者
论文摘要
在带有直侧的飞机多边形$ p $中，我们证明了固定，粘性和不可压缩的Navier-Stokes方程的Leray-HOPF解决方案的分析规律性。我们假设小数据，分析量力和无滑动边界条件。分析规则性在具有均匀规范的所谓规范，角度加权空间中进行量化。这种分析规律性的含义包括kolmogorov $ n $ widths解决方案的指数较小，混合$ hp $ $ hp $ didules的Galerkin有限元和频谱元素离散和模型订单减少技术的指数收敛速率。
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 of model order reduction techniques.
