Analytic regularity for the incompressible Navier-Stokes equations in polygons

Abstract

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.