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

We investigate the analytic regularity of the Stokes problem in a polygonal domain Omega subset of 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. (c) 2005 Elsevier B.V. All rights reserved.