Analytic regularity for the incompressible Navier-Stokes equations in polygons

04/23/2020

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by   Carlo Marcati, et al.

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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.