Analytic regularity of Stokes flow in polygonal domains

Abstract

We investigate the analytic regularity of the Stokes problem in a polygonal domain $\Omega \subset R^2$ with straight sides and piecewise analytic data. We establish a shift theorem in weighted Sobolev spaces of arbitrary order with explicit control of the order-dependence of the constants. The shift-theorem in countably normed weighted Sobolev spaces implies in particular interior analyticity and Gevrey-type analytic regularity near the corners.