Analytic regularity of Stokes flow on polygonal domains in countably weighted Sobolev spaces

Abstract

We investigate the analytic regularity of the Stokes problem in a polygonal domain Ω ⊂ 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 the framework of countably weighted Sobolev spaces implies in particular interior analyticity and Gevrey-type analytic regularity near the corners.