Analytic Regularity of Solutions to the Navier–Stokes Equations with Mixed Boundary Conditions in Polygons

.We prove weighted analytic regularity of Leray–Hopf variational solutions for the stationary, incompressible Navier–Stokes equations (NSEs) in plane polygons, subject to analytic body forces. We admit mixed boundary conditions which may change type at each corner. The weighted analytic regularity results are established in scales of corner-weighted Kondrat'ev spaces of finite order. The proofs rely on a priori estimates for the corresponding linearized boundary value problem in sectors in corner-weighted Sobolev spaces and on an induction argument for the weighted norm estimates on the quadratic nonlinear term in the NSE in a polar frame.KeywordsNavier–Stokes equationspolygonsanalytic regularitymixed boundary conditionsMSC codes35Q3076N1035A20